What’s the answer I need help pls?

Answer:

Answer: C) 19

We can solve this problem using the following chain of thought reasoning:

Step 1: We know that the ratio of Big Dogs to Small Dogs is 5 to 4. Therefore, if there are 15 Big Dogs in total, then the total number of Dogs in the park must be the sum of the Big Dogs and the Small Dogs.

Step 2: Since we know the ratio of Big Dogs to Small Dogs is 5 to 4, we can solve for the number of Small Dogs in the park: 15 (Big Dogs) / 5 = 3. Therefore, the total number of Dogs in the park is 15 + 3 = 18.

Step 3: Lastly, since we know that the total number of Dogs in the park is 18, the number of Small Dogs in the park can be found by subtracting the number of Big Dogs from the total: 18 - 15 = 3.

Therefore, the answer is C) 19 Small Dogs at the Dog Park.

Answer:

option B

Step-by-step explanation:

big : small

5 : 4

5 units= 15

1 unit= 15÷5

= 3

4 units= 3×4

= 12

there are 12 small dogs at the dog park

The equation of the tangent line to the curve x² + x²y² + y = 1 at the point where x=-1 is (-dx/dy + 2)/(1 - √5)(x + 1). The interval of concavity for f(x) = xlnx is (0, ∞) and there are no points of inflection.

To find the equation(s) of the tangent line(s) to the curve x² + x²y² + y = 1 at x = -1, we need to find the derivative of the curve with respect to x, i.e.,

2x + 2xy²(dx/dy) + dy/dx = 0

At x = -1, we get

-2 + 2y²(dy/dx) + dx/dy = 0

dy/dx = (-dx/dy + 2)/(2y²)

Now, substituting x = -1 in the curve, we get

1 - y + y² = 0

Solving for y, we get

y = (1 ± √5)/2

Substituting y = (1 + √5)/2 in the equation for dy/dx, we get

dy/dx = (-dx/dy + 2)/(2(1 + √5)/4) = (-dx/dy + 2)/(√5 + 1)

Therefore, the equation of the tangent line to the curve at x = -1, y = (1 + √5)/2 is

y - (1 + √5)/2 = (-dx/dy + 2)/(√5 + 1)(x + 1)

Similarly, substituting y = (1 - √5)/2 in the equation for dy/dx, we get

dy/dx = (-dx/dy + 2)/(1 - √5)

Therefore, the equation of the tangent line to the curve at x = -1, y = (1 - √5)/2 is

y - (1 - √5)/2 = (-dx/dy + 2)/(1 - √5)(x + 1)

To find the intervals of concavity and any point(s) of inflection for f(x) = xlnx, we need to find the second derivative of the function with respect to x, i.e.,

f''(x) = (d²/dx²)(xlnx) = d/dx(lnx + 1) = 1/x

Now, to find the intervals of concavity, we need to find the values of x for which f''(x) > 0 and f''(x) < 0. We have

f''(x) > 0 when x > 0, which means the function is concave up on (0, ∞).

f''(x) < 0 when x < 0, which means the function is concave down on (0, ∞).

To find any point(s) of inflection, we need to find the values of x for which f''(x) = 0. However, in this case, f''(x) is never equal to zero. Therefore, there are no points of inflection for the function f(x) = xlnx.

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Answer:

The distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.

Step-by-step explanation:

Since the distance between any two parallel streets along King Street or Queen Street is always about 1.42 km, the distance along Park Street from King Street to Queen Street is:

1.42 km + 1 km + 1.42 km = 3.84 km

Similarly, the distance along Albert Street from King Street to Queen Street is:

1 km + 1.42 km + 1 km = 3.42 km

Therefore, the difference in distance is:

3.84 km - 3.42 km = 0.42 km

So, the distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.

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The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.

Let's denote the length of the bookmark as L and the width as W.

The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.

From the given information, we have two equations:

Equation 1: A = 150 square centimeters

Equation 2: P = 62 centimeters

Substituting the formulas for area and perimeter, we get:

Equation 1: L * W = 150

Equation 2: 2L + 2W = 62

To solve these equations, we can use substitution or elimination. Let's solve by substitution:

From Equation 1, we can express one variable in terms of the other:

L = 150 / W

Substituting this into Equation 2:

2(150 / W) + 2W = 62

300 / W + 2W = 62

300 + 2W^2 = 62W

2W^2 - 62W + 300 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

[tex]2W^2 - 62W + 300 = 0[/tex]

(W - 10)(2W - 30) = 0

This gives us two possible solutions:

W - 10 = 0 -> W = 10

2W - 30 = 0 -> W = 15

Since the width cannot be longer than the length, we discard the solution W = 15.

So, the width of the bookmark is W = 10 centimeters.

Now, we can substitute this value into Equation 1 to find the length:

L * 10 = 150

L = 150 / 10

L = 15

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The probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 11/12

To calculate the probability of rolling two fair six-sided dice and getting a sum of 4 or higher, we first need to calculate the total number of possible outcomes.

The number of possible outcomes when rolling two dice is 6 × 6 = 36, since each die has 6 possible outcomes.

Now, let's find the number of outcomes that result in a sum of 4 or higher. We can do this by listing all the possible outcomes:

Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes

Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes

Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes

Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes

Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes

Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes

Sum of 10: (4, 6), (5, 5), (6, 4) = 3 outcomes

Sum of 11: (5, 6), (6, 5) = 2 outcomes

Sum of 12: (6, 6) = 1 outcome

Therefore, the number of outcomes that result in a sum of 4 or higher is 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.

Therefore, the probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 33/36 = 11/12.

To find the probability of getting a sum of 44 or higher, we need to subtract the probability of getting a sum of 43 or lower from 1:

Sum of 2: (1, 1) = 1 outcome

Sum of 3: (1, 2), (2, 1) = 2 outcomes

Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes

Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes

Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes

Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes

Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes

Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes

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The percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3 %

the percent change in carbon dioxide According to a WMO report in 2019 greenhouse gas concentrations, it was discovered that carbon dioxide growth rates were nearly 20% higher than the previous five years and that the percentage increase from 2015 and 2019 was approximately 2.88%. which is approximately 3 %.

carbon dioxide in the atmosphere in 2015 = 399 parts per million

carbon dioxide in the atmosphere in 2019 = 410.5 parts per million

Percentage change can be calculate by using

% change = [tex]\frac{Final - initial }{initial}[/tex] × 100

% change = [tex]\frac{410.5 - 399}{399} \[/tex] × 100

% change = 2.88 %

Hence, the percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3%

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The correct answer is b. 3%.

To answer this question, we need to compare the concentration of carbon dioxide in the atmosphere between 2015 and 2019. The concentration of carbon dioxide is measured in parts per million (ppm). In 2015, the concentration of carbon dioxide in the atmosphere was around 400 ppm, while in 2019, it was around 414 ppm.

To calculate the percent change between these two years,

Percent Change = [(New Value - Old Value) / Old Value] x 100%

Percent Change = [(414 - 400) / 400] x 100%

Percent Change = 3.5%

Therefore, the correct answer is b. 3%.

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To solve the equation 8 x five sixths, we first convert the fraction to a decimal by dividing the numerator (5) by the denominator (6), which gives us 0.83.

We then multiply 8 by 0.83 to get the final answer of 6.64. Therefore, 8 x five sixths = 6.64.

In general, to multiply a whole number by a fraction, we can convert the fraction to a decimal and then multiply the whole number by the decimal.

Alternatively, we can convert the whole number to a fraction with a denominator of 1 and then multiply the two fractions by cross-multiplying and simplifying.

In this case, we could also write 8 as 8/1 and multiply it by 5/6 to get (8 x 5)/(1 x 6) = 40/6, which simplifies to 6 and 4/6 or 6.67 (rounded to two decimal places). However, converting the fraction to a decimal is often simpler and more practical.

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Answer:

Step-by-step explanation:

An obtuse angle has a measure between 90 and 180 degrees. Looks like S and Q have obtuse angles, Its impossible to be sure unless you measure them with a protractor.

847 cubic feet of cement will be needed for the job.

To find the amount of cement needed for the cistern, we need to calculate the difference in volume between the outer and inner cylinders.

First, let's find the volume of the outer cylinder:
Outer radius (R) = (Inner diameter + 2 * Wall thickness) / 2 = (10 + 2 * 1) / 2 = 6 feet
Outer height (H) = 20 feet
Outer cylinder volume (V1) = π * R^2 * H = 3.14 * 6^2 * 20 = 3.14 * 36 * 20 ≈ 2260.96 cubic feet

Next, let's find the volume of the inner cylinder:
Inner radius (r) = Inner diameter / 2 = 10 / 2 = 5 feet
Inner height (h) = Outer height - 2 * Wall thickness = 20 - 2 * 1 = 18 feet
Inner cylinder volume (V2) = π * r^2 * h = 3.14 * 5^2 * 18 = 3.14 * 25 * 18 ≈ 1413.72 cubic feet

Finally, subtract the inner cylinder volume from the outer cylinder volume to find the amount of cement needed:
Cement volume = V1 - V2 ≈ 2260.96 - 1413.72 ≈ 847.24 cubic feet

To the nearest cubic foot, approximately 847 cubic feet of cement will be needed for the job.

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a. The smallest value in the data set is 4 miles per hour. b. The largest value in the data set is 48 miles per hour. c. The median is 26 miles per hour.

a. The smallest value in the data set is 4 miles per hour.

b. The largest value in the data set is 48 miles per hour.

c. To find the median, we need to arrange the values in order from smallest to largest:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

The median is the middle value in this list. Since there are an even number of values, we take the average of the two middle values:

Median = (24 + 28) / 2 = 26

Therefore, the median speed of the 100 cars as they passed through the busy intersection is 26 miles per hour.

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Ruby and Emma can assemble one gift basket in 0.1818 minutes, together. They will finish the 54th basket at  7:27 PM.

To solve the problem, we first need to find how many gift baskets Ruby and Emma can assemble in one minute.

Ruby can assemble 2/22 = 1/11 gift basket in one minute.

Emma can assemble 4/44 = 1/11 gift basket in one minute.

Together, they can assemble 1/11 + 1/11 = 2/11 = 0.1818 (rounded to four decimal places) gift baskets in one minute.

To assemble the 54th gift basket, they need to assemble 53 gift baskets before that.

53 gift baskets / 0.1818 gift baskets per minute = 291.8181 minutes

Since they start at 1:00 p.m. and Emma starts 15 minutes later, they will finish 291.8181 minutes after 1:15 p.m., which is approximately 7:27 p.m.

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The amount of water needed for 1/3 cup of rice, is 3/4 cups of water.

The problem asks us to find out how much water is needed for 1/3 cup of rice, given that 2 1/4 cups of water are needed for 1 cup of rice. To solve this problem, we can use a proportion.

A proportion is an equation that says two ratios are equal. In this case, we want to set up a proportion that relates the amount of water needed to the amount of rice.

Let's start by writing down what we know. We know that for 1 cup of rice, we need 2 1/4 cups of water. We can write this as a ratio:

2 1/4 cups water : 1 cup rice

Now we want to figure out how much water we need for 1/3 cup of rice. Let's call the amount of water we need "x" (we don't know what it is yet), and set up another ratio:

x cups water : 1/3 cup rice

We can now set up our proportion by equating these two ratios:

2 1/4 cups water : 1 cup rice = x cups water : 1/3 cup rice

To solve for x, we can cross-multiply and simplify. Cross-multiplying means we multiply the numerator of one ratio by the denominator of the other ratio, like this:

(2 1/4 cups water) * (1/3 cup rice) = (x cups water) * (1 cup rice)

To simplify this, we can convert the mixed number 2 1/4 to an improper fraction:

2 1/4 = 9/4

Now we can substitute these values and multiply:

(9/4 cups water) * (1/3 cup rice) = (x cups water) * (1/1 cup rice)

Multiplying the fractions on the left-hand side gives:

9/12 cups water = (x cups water) * (1/1 cup rice)

Simplifying the fraction on the left-hand side gives:

3/4 cups water = x cups water

So we have found that x, the amount of water needed for 1/3 cup of rice, is 3/4 cups of water. Therefore, if you have 1/3 cup of rice, you would need to use 3/4 cups of water to cook it.

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If buying three movie tickets and a popcorn, which costs $5.50, is the same price as buying two tickets snacks worth a total of 16.50, one movie ticket costs $2.20.

Let the cost of one movie ticket be represented by x.

According to the problem, buying three movie tickets and a popcorn costs $5.50, so we can set up the equation:

3x + $5.50 = 2y

where y is the cost of snacks.

Similarly, buying two tickets and snacks worth a total of $16.50 can be represented by the equation:

2x + y = $16.50

We can solve this system of equations by substituting the first equation into the second equation for y:

2x + (3x + $5.50) = $16.50

5x + $5.50 = $16.50

5x = $11

x = $2.20

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The length of QR to the nearest tenth of a foot is approximately 92.3 feet.

To find the length of QR in AQRS, we can use the Law of Cosines. This formula relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we want to find QR, which is opposite the known angle ZQ.

So, let's write the formula:

QR² = SQ² + QS² - 2(SQ)(QS)cos(ZQ)

Substituting in the given values, we get:

QR² = 94² + QS² - 2(94)(QS)cos(41°)

We still need to find QS, but we can use the fact that ZS is a right angle to do so. Since ZQ and ZS are complementary angles (add up to 90°), we know that:

cos(ZQ) = sin(ZS)

So, we can rewrite the Law of Cosines formula as:

QR² = 94² + QS² - 2(94)(QS)sin(ZS)

Now we need to use the sine ratio to find QS. Since ZS is opposite the side SQ, we can write:

sin(ZS) = QS / SQ

Rearranging this equation gives:

QS = SQ sin(ZS)

Substituting in the values we know:

QS = 94 sin(90°)

Since sin(90°) = 1, we can simplify to:

QS = 94

Plugging this into our Law of Cosines equation:

QR² = 94² + 94² - 2(94)(94)sin(ZS)

QR² = 2(94)² - 2(94)²cos(41°)

QR² = 2(94)²(1 - cos(41°))

QR ≈ 92.3 feet (rounded to the nearest tenth)

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The total count of inches that a Kameron cover is 301.44 inches, under the condition that we have to  use 3.14 as an approximation of π.

The circumference formula of a circle is
C=πd

Here
C =  refers to circumference
d = refers to diameter.
Since we know that the spoke length is 16 inches, we can evaluate the diameter by multiplying it by 2. Hence, the diameter of the wheel is 32 inches.

Now that we know the diameter of the wheel, we calculate its circumference using the formula
C=πd.
Staging in this formula
d=32 inches
π=3.14

C = πd
= 3.14 x 32
= 100.48 inches

So Kameron covers 100.48 inches of ground in one full rotation of the unicycle wheel.
Now in order to evaluate  how many inches of ground Kameron covers in 3 full rotations of the unicycle wheel, we simply need to multiply this value by 3
100.48 x 3
= 301.44 inches

Thus, Kameron covers approximately 301.44 inches of ground in 3 full rotations of the unicycle wheel.

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The scientific notation 5.3*10‐⁵ in standard notation gives 0.000053

From the question, we have the following parameters that can be used in our computation:

Write 5.3*10‐⁵ in standard notation.

The above number is written in scientific notation

The standard notation of a number a * 10ⁿ is represented as

a000 where the 0's are in n places

Using the above as a guide, we have the following:

5.3 * 10‐⁵ = 0.000053

Hence, 5.3*10‐⁵ in standard notation is 0.000053

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Answer: To find the total amount of sugar required to make the banana pudding, we need to add the amount of sugar needed for the flour mixture to the amount of sugar needed for the meringue topping.

The recipe calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. To add these two fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can convert these fractions to twelfths:

2/3 = 8/12

1/4 = 3/12

Now we can add these two fractions:

8/12 + 3/12 = 11/12

So the total amount of sugar required to make the banana pudding is 11/12 of a cup.

The equations represent four different parabolas with different shapes and orientations, but all of them have the same axis of symmetry, which is the y-axis (because there is no x term).

The collection of all points in a plane that are equally spaced from a fixed line and another fixed point in the plane that is not on the line is known as a parabola. The focus of the parabola is the fixed point (F) and the fixed point (D) is known as the directrix.

The equation of a parabola in standard form is:

y = a x² + b x + c

where "a" is the coefficient of the quadratic term (x^2), "b" is the coefficient of the linear term (x), and "c" is the constant term.

Looking at the given equations:

So, the equations represent four different parabolas with different shapes and orientations, but all of them have the same axis of symmetry, which is the y-axis (because there is no x term).

To graph each parabola, you can use the vertex form of the equation:

y = a (x - h)² + k

where (h, k) is the vertex of the parabola.

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The ratio of the surface area to volume of a right rectangular prism with a square base and a height that is triple the base edge is 6:1.

Let x be the length of one side of the square base of the prism. Then the height of the prism is 3x. The surface area of the prism is given by 2x² + 4(x)(3x) = 14x², since there are two square faces with area x² each and four rectangular faces with area x(3x) each.

The volume of the prism is x²(3x) = 3x³. Therefore, the ratio of surface area to volume is (14x²)/(3x³) = 14/3x = 4.67/x. Since x is a length, it must be positive, so the ratio is minimized when x is as large as possible.

Therefore, the smallest possible ratio is when x approaches infinity, and in this limit, the ratio approaches 0. However, in the real world, x must be finite, so the ratio is always greater than 0.

We can see that the ratio decreases as x increases, so the smallest possible ratio occurs when x is as small as possible.

The smallest possible positive value of x is 0.000000...01, which is very close to 0 but not equal to 0. Therefore, the ratio is always greater than 0 but can be made arbitrarily small.

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The particular solution with the given initial condition is:

[tex]y = (5/ e^(16/3)) * e^(x^2/3)[/tex]

To find the particular solution, we need to first separate the variables in the differential equation:

[tex]dy/dx = x + (3/2)y[/tex]
[tex]dy/y = (2/3)x dx[/tex]

Next, we integrate both sides:

[tex]ln|y| = (1/3)x^2 + C[/tex]

where C is the constant of integration.

To find the value of C, we use the initial condition f(-4) = 5:

[tex]ln|5| = (1/3)(-4)^2 + C[/tex]
[tex]ln|5| = (16/3) + C[/tex]
[tex]C = ln|5| - (16/3)[/tex]

Therefore, the particular solution is:

[tex]ln|y| = (1/3)x^2 + ln|5| - (16/3)[/tex]
[tex]ln|y| = (1/3)x^2 + ln|5/ e^(16/3) |[/tex]
[tex]y = ± (5/ e^(16/3)) * e^(x^2/3)[/tex]

However, since we know that f(-4) = 5, we can eliminate the negative solution and obtain:

[tex]y = (5/ e^(16/3)) * e^(x^2/3)[/tex]

So the particular solution with the given initial condition is:

[tex]y = (5/ e^(16/3)) * e^(x^2/3)[/tex]

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Answer:

4/5

Step-by-step explanation:

In probability, if there are two events and "or" is used, we will add the probabilities of each event. Since the event that an odd number is spun does not affect whether a red number is spun, we can calculate the probability of each event separately:

Probability of spinning an odd number:

5/10        because there are 5 odd numbers possible & 10 outcomes

Probability of spinning a red number:

3/10        because there are 3 red numbers & 10 outcomes

Now add the probability of each event:

5/10 + 3/10 = 8/10 = 4/5

None of the given equations have infinitely many solutions.

To identify which equation does not have infinitely many solutions among the given options.

1) 0 = 6x + 4 = 2(3x + 2)
2) 2x + 5 - 5x + 2 + 3x = 7
3) -3x + 13 + 4x – 5 = 7x + 8
4) 4x - 8 = 2(2x + 3)

Let's analyze each equation:

1) The equation can be simplified to 0 = 6x + 4, which is not true for all x, so it does not have infinitely many solutions.
2) Simplifying the equation, we get 0 = 7, which is false for any x, so it does not have infinitely many solutions.
3) Simplifying the equation, we get 1x + 8 = 7x + 8, which can be further simplified to -6x = 0, or x = 0. Since it has only one solution, it does not have infinitely many solutions.
4) Expanding the equation, we get 4x - 8 = 4x + 6. It is false for any x, so it does not have infinitely many solutions.

Therefore, none of the given equations have infinitely many solutions.

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Answer:

60

Step-by-step explanation:

((sum of frequency of even numbers)/(total number of tries))(150)

Unilever should run a z-test of a proportion to test Proctor & Gamble's claim that at least half of the bars of Ivory soap they produce are 99.44% pure or more.

Unilever should use a z-test of a proportion to test whether Proctor & Gamble's claim that at least 50% of Ivory soap bars are 99.44% pure or more is statistically significant based on a sample of 146 bars, of which 70 meet the purity criteria.

The null hypothesis is that the proportion of Ivory soap bars meeting the purity criteria is 0.50, and the alternative hypothesis is that it is greater than 0.50. The z-test yields a p-value of 0.038, which is less than the significance level of 0.05.

Thus, Unilever has sufficient evidence to reject Proctor & Gamble's claim and conclude that the proportion of Ivory soap bars meeting the purity criteria is significantly different from 50%.

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Answer:

76

Step-by-step explanation:

If the mean of 28 numbers is 18 then the sum of those numbers=28×18=504

if one number is added then 29×20=580

the new number therefore=580-504=76

Answer:   C

Step-by-step explanation:

f moved left 4 spaces in x direction to get to g

so take opposite sign

f(x+4)

The probability is less than 0.489 is approximately 0.8980 or 89.80%  that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489

First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:

Mean = p = 0.48

Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071

Next, we need to standardize the sample proportion using the formula:

z = (sample proportion - population proportion) / standard deviation

z = (0.489 - 0.48) / 0.071 = 1.27

Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.

Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.

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The mass of copper in the platter is 45 grams, which corresponds to option (B).

What is ratio ?

In mathematics, a ratio is a comparison of two quantities, often expressed as a fraction. Ratios can be used to describe how two quantities relate to each other, and they can be used to make predictions and solve problems in a variety of contexts.

The ratio of silver to copper in the platter is 37:3 by mass, which means that for every 37 grams of silver, there are 3 grams of copper.

Let's call the mass of silver in the platter "s" and the mass of copper "c". We know that the total mass of the platter is 600 grams, so:

s + c = 600

We also know that the ratio of silver to copper is 37:3, which means that:

s÷c = 37÷3

We can use this second equation to solve for s in terms of c:

s:c = 37:3

s = (37÷3)c

Now we can substitute this expression for s into the first equation:

s + c = 600

(37÷3)c + c = 600

(40÷3)c = 600

c = (3÷40) * 600

c = 45

Therefore, the mass of copper in the platter is 45 grams, which corresponds to option (B).

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The particular solution is [tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex].

[tex]dy/dt + 2cy = t^2 + 1[/tex]

To find the general solution of this differential equation, we can start by finding the integrating factor, which is given by:

I(t) = e^(∫2c dt) = [tex]e^(2ct)[/tex]

Next, we can multiply both sides of the differential equation by the integrating factor I(t):

[tex]e^(2ct) dy/dt + 2ce^(2ct) y = (t^2 + 1) e^(2ct)[/tex]

We can now recognize the left-hand side as the product rule of the derivative of the product of y and I(t):

[tex](d/dt)(y e^(2ct)) = (t^2 + 1) e^(2ct)[/tex]

Integrating both sides with respect to t gives:

[tex]y e^(2ct) = ∫(t^2 + 1) e^(2ct) dt + C[/tex]

The integral on the right-hand side can be solved using integration by parts, and we get:

∫([tex]t^2[/tex] + 1) [tex]e^(2ct) dt = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]

where K is an arbitrary constant of integration.

Substituting this expression back into the previous equation, we get:

[tex]y e^(2ct) = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]

Dividing both sides by e^(2ct), we obtain the general solution:

[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + Ke^(-2ct)[/tex]

where K is an arbitrary constant.

To find the particular solution that satisfies y(0) = 2, we can substitute t = 0 and y(0) = 2 into the general solution and solve for K:

[tex]y(0) = (1/2c) (0^2/2 + 0/2 + 1/2c) + Ke^(0)[/tex]

2 = 1/(4c) + K

Solving for K, we get:

K = 2 - 1/(4c)

Substituting this value of K back into the general solution, we get the particular solution:

[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex]

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