The difference 3 1/2 minus 1 1/2 must be
between and

Answer:

8 1/4

Step-by-step explanation:

8+(7+1)2 ÷ 4 · (1/2)^4

8+16 / 4 · 1/16

8+4 · 1/16

8+ 1/4 = 8 1/4

Answer:

Dilation by a scale factor of 3 followed by reflection about the y-axis.

Step-by-step explanation:

Let's start by considering the three sides of the right-angled triangle that is being created. According to the problem, the longest board is 10 feet, and the shortest board is 6 feet.

The remaining board's length is denoted by x feet. Let us use the Pythagorean theorem to solve for the missing side of the triangle:

a² + b² = c² where a and b are the two shorter sides of the triangle, and c is the hypotenuse. Therefore, applying this formula, we get:

6² + x² = 10²x²

= 100 - 36x²

= 64x

= ±√64x

= ±8

Ignoring the negative value for x, content loaded Martin and his aunt are building a wooden planter for her flowers in the shape of a right triangle for his aunt’s house. For the perimeter, he has calculated the longest board to be 10 feet and the shortest board to be 6 feet.  we can say that the missing side of the triangle is 8 feet long. Therefore, the length of the remaining board is 8 feet. The remaining board's length is denoted by x feet. Let us use the Pythagorean theorem to solve for the missing side of the triangle: a² + b² = c² where a and b are the two shorter sides of the triangle In conclusion, the length of the remaining board is 8 feet.

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Answer:

100/x/100

Step-by-step explanation:

Step-by-step explanation:

If the perimeter of the isosceles triangle is 12 cm, then the base of the triangle (x), as well as the length of the triangle leg (x) is 4 cm.

An isosceles triangle is a type of triangle in which two sides have the same length. These two equal sides are referred to as the legs of the triangle, while the remaining side is known as the base.

The perimeter of a triangle is the sum of the lengths of all its sides. In this case, since the triangle is isosceles, the base and one leg have the same length (x), and the other leg also has the same length (x). Therefore, the perimeter of the triangle is 2x + x = 3x. Given that the perimeter of the isosceles triangle is 12 cm, then:

3x = 12

 x = 12/3

 x = 4

So, the base and legs of the isosceles triangle each have a length of 4 cm.

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Your question seems to be missing the value for the perimeter of the triangle, but I suppose the complete question was:

"The length of the base of an isosceles triangle is x. The length of a leg is x. The perimeter of the triangle is 12 cm. Find x."

Answer:

-4/3

Step-by-step explanation:

If the slope of line a is 3/4, then the slope of line b will be -4/3.

a)  A(5) = 10 * e^(-0.05*5)

b)  7.776

To solve the given problem, the initial amount of chlorine should be assumed as 'P0' and the exponential function should be written in the form of y = P_0 * e^(kt) where P_0 is the initial amount of chlorine and k is the rate of change. Therefore, for the given problem, the exponential function can be given by: y = P_0 * e^(-0.05t) where P_0 is the initial amount of chlorine and t is the number of hours. This equation will give the amount of chlorine remaining after t hours. The formula for exponential decay is given by:A(t) = A₀ * e^(-kt) Where A(t) is the amount after time t, A₀ is the initial amount, k is the rate of decay, and t is the time elapsed. To calculate the remaining amount of chlorine after a certain number of hours, we'll utilize the formula above .Let's start with the given information: An exponential function that gives the amount of chlorine remaining after t hours is to be found. P₀ = the initial amount of chlorine, which is 10.We can also figure out the rate of decay from the given information. The amount of chlorine is reduced by 5% per hour, which means the rate of decay is 0.05. We need to put a negative sign in front of the rate of decay to indicate that it is decreasing. Let's use the formula to find the amount of chlorine remaining after 5 hours. Then, substitute A₀ = 10, k = -0.05, and t = 5 into the equation above to obtain A(5) = 10 * e^(-0.05*5) = 7.776.So, the amount of chlorine remaining after 5 hours is 7.776.

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According to the above, Pinocchio's nose would be 27 cm long.

To calculate the length of Pinocchio's nose we must perform the following procedure:

We start at 9cm, so we must multiply the length that increases for each lie by the number of lies and add the increase after it says 3 lies.

Then we must multiply the length that decreases for each truth and subtract how much his nose was reduced by telling two truths.

According to the above, Pinocchio's nose was 27 cm.

Note: This question is incomplete. Here is the complete information:

when pinocchio lies, his nose gets 8cm longer. when he tells the truth, his nose gets 3cm shorter. When his nose was 9cm long, he told three lies and made two true statements. how long was pinocchio's nose afterwards?

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Gene is incorrect in his statement. Let's compare the two numbers -2 1/8 and -2.25.Gene's claim that -2 1/8 is less than -2.25 is incorrect based on the numerical comparison of the two values.

To compare these numbers, we can convert them to a common format. -2 1/8 can be written as a decimal by dividing 1 by 8 and adding it to -2:

-2 1/8 = -2 + 1/8 = -2 + 0.125 = -2.125

Now let's compare -2.125 and -2.25. Both numbers are negative, so we can compare their absolute values instead.

|-2.125| = 2.125

|-2.25| = 2.25

Since 2.125 is less than 2.25, it means that -2.125 is less than -2.25. Therefore, Gene's statement that -2 1/8 is less than -2.25 is incorrect.

In decimal form, -2.125 is closer to 0 than -2.25. The value -2.125 is actually greater than -2.25 because the closer a number is to 0, the greater it is in the negative direction.

Therefore, Gene's claim that -2 1/8 is less than -2.25 is incorrect based on the numerical comparison of the two values.

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Answer:

$223.45

Step-by-step explanation:

premium fuel: 4.59 x 545

= 2501.55

regular fuel: 4.18 x 545

=2278.1

2501.55-2278.1 = 223.45

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

The engineer's improved light bulb likely has a statistically significant longer lifetime than the previous design, with a small but measurable difference of 0.2 hours.

Statistical significance refers to the probability that the observed difference between two groups (in this case, the old light bulbs and the new ones) is not due to chance alone. If the probability is low enough, we can confidently reject the null hypothesis (that there is no difference between the two groups) and conclude that there is a real difference between them.

In this case, a sample size of 40,000 bulbs is quite large, which increases the statistical power of the test and allows for even small differences to be detected as significant. The fact that the new bulb had a slightly longer lifetime of 1,200.2 hours, compared to the old bulb's average lifetime of 1,200 hours, suggests that the engineer's design improvement was successful in making the bulb last longer.

However, it's important to note that while the effect is statistically significant, the practical significance may be less clear. A difference of 0.2 hours may not make a noticeable impact on the bulb's usefulness or longevity in real-world scenarios. Additionally, other factors such as cost or energy efficiency may also need to be considered when evaluating the success of the new design.

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Answer:

Hi! The answer to your question is (2,-3)

Step-by-step explanation:

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☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

The standard error of the sample mean is 1.21.

Given;

Suppose a diet regimen for men results in an average weight loss of between 13. 4 and 18. 3 pounds, according to a 95% confidence interval. These findings were based on a group of 42 men who were classified as overweight at the beginning of the four-month trial.

A 95% confidence interval for a population mean is (13.4, 18.3)

Upper limit = 18.3

Lower limit = 13.4

Since population SD is unknown, this interval is constructed using the t distribution.

n = 42

c = 0.95

∴ α = 1 - c = 1 - 0.95 = 0.05

α/2 = 0.025

Also, d.f = n - 1 = 42 - 1 = 41

∴ ta/2.d.f =  ta/2.n-1  =  t0.025,41  =  2.02 . . . . use t table

Now,

The margin of error = (Upper limit - Lower limit)/2

                                 = (18.3 - 13.4)/2

                                 = 2.45

But,

Margin of error = ta/2.d.f-  * (s / \sqrt{} n)

Margin of error = ta/2.d.f-  * Standard error

2.45 = 2.02 * Standard error

Standard error = 1.2129

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Answer:

35 as a fraction is 7/20

Step-by-step explanation:

Answer:

11/35

Step-by-step explanation:

Step-by-step explanation:

it is given, AD=DC (S),

:. <DAB=<DCB (A) isosceles triangle,

and, <ADB=<CDB (A) BD bisector of <D.

So, by A-S-A criterion we can prove that triangle ( give it in sign) ABD = triangle ( give it in sign) CBD.

Hence, we can say that <ABD is not equal to <CDB.

Hope this helps you.

Answer:

See below.

Step-by-step explanation:

-10.75(20x+15.2)

-215x-163.4

-hope it helps

The equivalent expression is,

⇒ - 215x - 163.4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - 10.75 (20x + 15.2)

Now, We can simplify as;

⇒ - 10.75 (20x + 15.2)

⇒ - 10.75 × 20x - 10.75 × 15.2

⇒ - 215x - 163.4

Thus, The expression is equivalent to - 215x - 163.4.

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The least expensive C.A.R.S. that can be built to those specifications has dimensions of approximately 4.3088 m x 2.1544 m x 1.7321 m and will cost about $265.47 to build.

Let's start by looking at the dimensions of the base. We know that the length of the base is twice its width. Let's represent the width of the base as "x." This means that the length of the base is "2x." The area of the base is simply the product of the length and the width, which is 2x * x = 2x².

Next, let's look at the dimensions of the sides. The height of the box is going to be represented by "h." The length of each side is going to be equal to the length of the base, which we already know is 2x. The width of each side is going to be equal to the width of the base, which is just x. So the area of each side is simply 2hx.

Now we can use the formula for the volume of a rectangular prism to find the value of "h" in terms of "x." The volume of the box is given as 10 m^3, so:

V = lwh = (2x)(x)(h) = 10

Simplifying this equation, we get:

2x²h = 10

Solving for "h," we get:

h = 5/x²

Now that we have an expression for "h" in terms of "x," we can use it to find the total surface area of the box, which is the sum of the area of the base and the area of the four sides. We can then use this expression to find the minimum cost for a given volume of the box.

The total surface area of the box is given by:

A = 2x² + 4(2hx)

Substituting the expression we found for "h" into this equation, we get:

A = 2x² + 4(2x)(5/x²)

Simplifying this equation, we get:

A = 2x² + 40/x

Now we can take the derivative of this expression with respect to "x" and set it equal to zero to find the value of "x" that will minimize the cost of the box. Differentiating and setting equal to zero, we get:

dA/dx = 4x - 40/x² = 0

Solving for "x," we get:

x^3 = 10

Taking the cube root of both sides, we get:

x ≈ 2.1544

Now we can use this value of "x" to find the dimensions of the least expensive C.A.R.S. that can be built to those specifications. The length of the base is twice the width, so:

Length = 2x ≈ 4.3088

Width = x ≈ 2.1544

Height = 5/x² ≈ 1.7321

So the dimensions of the least expensive C.A.R.S. that can be built to those specifications are approximately: Length = 4.3088 m Width = 2.1544 m Height = 1.7321 m

These dimensions will allow us to build a C.A.R.S. with a volume of 10 m^3, while using the least amount of material possible, which means that the cost will be minimized. We can verify this by calculating the total surface area of the box and the cost of the materials needed.

The total surface area of the box can be calculated by substituting the values we found for "x" and "h" into the expression we derived earlier:

A = 2(2.1544)² + 4(2)(5)/(2.1544)² ≈ 28.2742 m²

Now we can calculate the cost of the materials needed to build the box:

Cost = (Area of base)(Cost per square meter for base) + (Area of sides)(Cost per square meter for sides)

Cost = (2.1544²)(10) + (28.2742 - 2(2.1544²))(6) ≈ $265.47

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Answer:

Y = 4x

Step-by-step explanation:

In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.

99^2= 99*99

99

x 99

--------

891 (Multiplying 99 by 9)

891 (Multiplying 99 by 9 and leaving a space on the right)

--------

9801 (Adding)

The answer is 9801.

at a map scale of 1:1500, 12 centimeters on the map is equivalent to 1.8 kilometers on the ground.

step-by-step

since the scale is 1 to 15,000 you simply multiply it by the 12 cm

12cm × 15,000 = 180,000

but you still have to convert it to kilometers (the measurement on the ground).

to go from centimeters to kilometers move the decimal 5 place values to the left.

final answer

1.8 kilometers

The smallest measurement used in the apothecary system for volume is the minim.

The apothecary system is an outdated system of measurements primarily used in pharmacy and medicine. It includes various units for measuring volume, weight, and other quantities.

In the apothecary system, the minim is the smallest unit of measurement for volume. It is equivalent to approximately 0.0616 milliliters.

The minim is a small unit of measurement and is typically used for precise dosing of liquids in the apothecary system. It is commonly used in pharmaceutical compounding and in the preparation of medications.

However, it's important to note that the apothecary system is no longer widely used in modern healthcare practices. The metric system, with units such as milliliters and liters, has become the standard for measuring volume in most countries.

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Answer:

a variable.

Step-by-step explanation:

I know this because I had a test today that I studied for but I of course failed it…

It was for math.

Answer:

A B

Step-by-step explanation:

In this problem, we have a set of the coordinates of two pairs of points, and we must compute the slope for each one of the sets.

For the line that passes through points (x₁, y₁) and (x₂, y₂), the slope is:

(11) (x₁, y₁) = (5, -2) and (x₂, y₂) = (6, -5)

Replacing the coordinates of these points in the formula above, we get:

(12) (x₁, y₁) = (3, 8) and (x₂, y₂) = (-4, 8)

Replacing the coordinates of these points in the formula above, we get:

A slope equal to zero represents an horizontal line.

(13) (x₁, y₁) = (7, 2) and (x₂, y₂) = (7, 4)

Replacing the coordinates of these points in the formula above, we get:

A slope equal to infinity represents a vertical line.

11. m = -3

12. m = 0 (horizontal line)

13. m = ∞ (vertical line)

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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Answer:

Step-by-step explanation:

hello : x-3y=-9 ...(*)

        -3x+9y=12...(**)

divided (**) by 3 : -x+3y =4 ...(**)

add(*) and(**) : 0=4  ..(false)

no reals solutions