Solve the simultaneous equations:
y=x² + 3x - 18
x + 2y + 14 = 0

The term for the probability that a value falling outside the control limits is still due to normal variation is called the Type I error or the alpha error.

The term for the probability that a value falling outside the control limits is still due to normal variation is called the Type I error or alpha error.

It refers to the probability of rejecting a true null hypothesis (in this case, the process is in control) when it should not be rejected. In other words, it is the probability of concluding that there is a problem with the process when there is actually no problem, and the observed value is simply a result of random variation.

This means that the value appears to be abnormal, but it is actually just a result of the natural variation in the process. It is important to minimize the risk of Type I errors to ensure that only truly abnormal values are addressed and corrected.

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The length of the side w is 55mm. Option C

Note that the different trigonometric identities are;

From the triangle shown, we have;

x = 45mm

z = 80mm

We also have tangent where the star is located is 1

Then,

tan θ = 1

find the tangent inverse of the values

θ = 45 degrees

As given in the diagram, the diagrams are similar

So both angles are 45 degrees

However, we can deduce that since the angles are equal, then, the sides are equal

x = w = 55mm

w = 55mmm

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volumes from liters (L) to milliliters (mL), you can use the conversion factor that 1 L is equal to 1000 mL.

Knowing the relationship between the two units will make converting between litres and millilitres simple. Both litres and millilitres are measurements of a liquid's volume.

The basic measure of liquid capacity is the litre. The liquid volume can also be measured in millilitres, centilitres, and kilolitres. All of these units have different values from one another.

Similar to millilitres, litres also denote volume, however one litre is equivalent to one thousand millilitres (1 L = 1000 mL).

To convert the given volumes from liters (L) to milliliters (mL), you can use the conversion factor that 1 L is equal to 1000 mL. Here are the conversions:

4.27 L = 4.27 x 1000 mL = 4270 mL

0.35 L = 0.35 x 1000 mL = 350 mL

0.06 L = 0.06 x 1000 mL = 60 mL

9.05 L = 9.05 x 1000 mL = 9050 mL

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Answer:

1.2 tsp

Step-by-step explanation:

6x0.2=1.2

There are 6 mL,and if each mL is 0.2tsp, then you have to multiply.

Answer:

Option i) At least 64 of the numbers are greater than or equal to 35 must be true

Since the median is 35, we know that there are 63 numbers greater than 35 and 63 numbers smaller than 35. However, since there is an odd number of total numbers (127), the median itself must be included in one of these groups. Therefore, there are at least 64 numbers that are greater than or equal to 35.

Answer:

In (-3)^2, Henry multiplied -3 by 2. That is not correct. (-3)^2 = (-3)(-3) = 9. Additionally, a^3 • a^4 = a^7, and so

[tex] {( - 5ab)}^{3} \times {( - 3 {a}^{2} {b}^{2} )}^{2} [/tex]

[tex] {( - 5)}^{3} {a}^{3} {b}^{3} \times ( { - 3)}^{2} {a}^{4} {b}^{4} [/tex]

[tex]( - 125 \times 9) {a}^{7} {b}^{7} = 1125 {a}^{7} {b}^{7} [/tex]

Answer:

name of figure : pyramid

volume : 200yds.

Step-by-step explanation:

The formula for volume of a pyramid is 1/3(lwh), in this case, it would be 1/3(12x5x10). 12x5x10 is 600, and 1/3 of 600 is 200. Therefore, the volume is 200yds.

IM VERY SORRY IF THIS DIDN'T MAKE SENSE!

Answer:

Step-by-step explanation:

It should be 177.88

According to the given data the length of the cable is 257.6ft.

An angle is formed by two rays, also called sides or arms, that extend from the vertex in different directions. The amount of turn between the two rays is the angle's measure, usually expressed in degrees or radians. A full turn, or a complete revolution, is 360 degrees or 2π radians.

To find the length of the cable, we can use trigonometry. Let "x" be the length of the cable. The tower height forms a right angle with the ground, so we can use the sine function:

sin(50) = opposite/hypotenuse

sin(50) = height/x

We know the height of the tower is 200 ft, so we can solve for x:

x = height/sin(50)

x = 200/sin(50)

x ≈ 257.6 ft

Therefore, the length of the cable is approximately 257.6 ft.

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Probable and certain both speak about something that may (or may not) happen in the future, but probable and possible speak about future possibilities in different ways.

‘Probable’ is high up on the scale of probability.  If something is probable, then there is a high chance that something will happen.  We can imagine that ‘probable’ is around 80% and up on the scale of probability.

If something is possible, it doesn’t mean it’s probable.  However, if something is probable then it’s possible too.  And if this confuses you then you’re probably in the right place.  

Probable and certain are both on a scale of probability.  Probability is the level of possibility or chance that something will happen or will be true in the present or future.  

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Answer:

607,532

The number "six hundred and seven thousand five hundred and thirty-two" can be written in figures as 607,532.

Therefore, it takes four days for the rain gauge to be free of water. The answer is option D, day 7.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation usually contains one or more variables, which are symbols that represent unknown or varying quantities. The values of the variables that satisfy the equation are called the solutions of the equation.

Here,

Let's start by finding out how much water is left in the gauge after one day of evaporation and addition. If the rain gauge had 10 inches of water at the start of the week, then after one day:

4 inches of water would have evaporated, leaving 10 - 4 = 6 inches of water.

2 more inches of rain would have fallen, bringing the total to 6 + 2 = 8 inches of water.

So after one day, the rain gauge has 8 inches of water.

Now we need to repeat this process until there is no water left in the gauge.

After the second day:

4 more inches of water would have evaporated, leaving 8 - 4 = 4 inches of water.

2 more inches of rain would have fallen, bringing the total to 4 + 2 = 6 inches of water.

After the third day:

4 more inches of water would have evaporated, leaving 6 - 4 = 2 inches of water.

2 more inches of rain would have fallen, bringing the total to 2 + 2 = 4 inches of water.

After the fourth day:

4 more inches of water would have evaporated, leaving 4 - 4 = 0 inches of water.

2 more inches of rain would have fallen, but it would not have filled the gauge since it was already empty.

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Answer:

6/6=1

Step-by-step explanation:

The Results:

a) The measure of ∠BDC = 67°

b) The measure of arc DAC = 46°

a) The measure of ∠BDC

Since DC ⊥ AB, ∠DCB is a right angle, which means it measures 90°. Also, given that m∠DCB = 23, we can use the fact that the angles in a triangle sum to 180° to find ∠DBC.

∠DBC + ∠DCB + ∠B = 180 (angles in a triangle sum to 180)

∠DBC + 90 + 23 = 180 (substituting values)

∠DBC = 180 - 90 - 23 = 67°.

Thus, the measure of ∠BDC = 67°

b) The measure of arc DAC:

Since AB = AC, it implies that ∠ABC = ∠ACB (angles opposite to equal sides of an isosceles triangle are equal). Therefore, ∠ACB is also 23°.

Now, since ∠ACB is an inscribed angle that intercepts the arc DAC, the measure of the arc DAC is twice the measure of ∠ACB.

Arc DAC = 2 × ∠ACB = 2 × 23 = 46°.

Therefore, the measure of arc DAC is 46°.

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The trig function that meets the given criteria is determined as f(x) = 4sin(π/4x) + 9.4.

We can use the formula for a sinusoidal function of the form:

f(x) = Asin(Bx - C) + D

where:

We have A = 4 and K = 9.4, so we know that the midline of the function is at y = D = 9.4.

Since we don't have any information about the horizontal shift, we can assume that C = 0.

Then, the formula becomes:

f(x) = 4sin(Bx) + 9.4

Now, we need to find B so that the function has a period of 2π. Since the period is given by T = 2π/B, we have:

2π = TB = (13.4 - 5.4)B = 8B

Therefore, B = π/4. Finally, we can write the function as:

f(x) = 4sin(π/4x) + 9.4

This function has an amplitude of 4, a midline at y = 9.4, and a period of 2π.

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Therefore, the simplified sum of the expression 7 1/4 and 4 5/12 is 35/3 that is option D, 11 2/3.

In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve arithmetic operations, algebraic operations, functions, and variables.

Here,

To add these mixed numbers, we need to first convert them to improper fractions with the same denominator:

7 1/4 = 28/4 + 1/4

= 29/4

4 5/12 = 48/12 + 5/12

= 53/12

Now, we can add the fractions:

=29/4 + 53/12

To find a common denominator, we can multiply the denominator of the first fraction by 3 and the denominator of the second fraction by 1:

29/4 × 3/3 = 87/12

53/12 × 1/1 = 53/12

Now we have the same denominator, so we can add the numerators:

87/12 + 53/12 = 140/12

We can simplify by dividing the numerator and denominator by their greatest common factor, which is 4:

140/12 ÷ 4/4 = 35/3

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The number of people that prefer mustard is 900 and the graphical representation of a datasets are box plots & circle graphs

The histogram is not given and the data represented on the histogram are not properly presented

This means that the histogram cannot be interpreted

Here, we have

Ketchup = 63

Mustard = 27

Chili = 60

So, we have

Mustard = 27/(63 + 27 + 60) * 5000

Evaluate

Mustard = 900

This means that 900 people prefer mustard

Given that

Data = Milligrams of Vitamin C from 100 different gummy vitamins sold

This data can be represented using a box plot because the five-summary data can be easily identified from the dataset

From the five-summary, the median can be derived

In this case, the graph to use is a circle graph

This is so because the circle graph would show the proportion of the student's preferences

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We can see here that the displays that can be used to display the data set of the water districts are:

The data set of the water districts is:

Data refers to any information or facts that can be collected, stored, and analyzed. This can include a wide range of things, such as numbers, text, images, audio recordings, and more.

Data can be used to provide insights, make decisions, and drive actions in a variety of fields, including science, business, medicine, and more. In order to be useful, data needs to be organized, structured, and analyzed in a way that can provide meaningful insights and information.

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The independent variable in the study examining the difference in 40 yard dash times between collegiate soccer, football, and cross-country players is the type of sport played by the athletes.

The coach is interested in comparing the 40 yard dash times of athletes from three different sports: soccer, football, and cross-country.

In this study, the independent variable is manipulated by selecting participants from each of the three sports. The athletes' 40 yard dash times will be the dependent variable, which is expected to vary based on the independent variable (i.e., the type of sport played by the athletes).

By comparing the 40 yard dash times of athletes from different sports, the coach can gain insights into how different types of athletic training and conditioning may affect speed and agility.

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A scatter plot or a line graph could be used to represent the relationship between the two variables.

A scatter plot is a graph in which each data point is represented by a dot on the graph. In this case, the data points would represent the amount of money spent on groceries and the percentage of that money spent on fruits and vegetables. Each data point would be plotted based on its corresponding values for the two variables, with the horizontal axis representing the amount of money spent on groceries and the vertical axis representing the percentage of that money spent on fruits and vegetables. The scatter plot would allow us to see if there is any relationship between the two variables, such as whether people who spend more on groceries tend to spend a higher percentage of that money on fruits and vegetables.

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The equation in the interval [0, 2π) 3csc^2x=4 are: x = π/3 and x = 2π/3.

We can start solving the equation by isolating the csc^2(x) term, using the fact that csc^2(x) = 1/sin^2(x):

3csc^2(x) = 4

csc^2(x) = 4/3

1/sin^2(x) = 4/3

sin^2(x) = 3/4

Taking the square root of both sides, we get:

sin(x) = ±√(3/4) = ±(√3)/2

Since we are looking for solutions in the interval [0, 2π), we need to determine the angles in this interval whose sine is equal to ±(√3)/2. These angles are π/3 and 2π/3, since sin(π/3) = √3/2 and sin(2π/3) = √3/2.

Therefore, the solutions in the interval [0, 2π) are:

x = π/3 and x = 2π/3.

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y = (-4/3)x + 1 this line will intersect point (3,-3) and be perpendicular to the line y = (3/4)x + 5.

y = (3/4)x + 5

Compare with the standard form of equation y = mx +c

3/4 is the slope.

The negative reciprocal of the slope is used to obtain a perpendicular slope.

-4/3 is the perpendicular slope.

Let's rewrite the equation: y = (-4/3)x + b

Remember that b is the line's y-intercept base. If the line must pass straight through the point (3, -3), we must determine the location of the base.

To accomplish this, we just enter our point into the formula and solve for our base.

-3 = (-4/3)(3) + b

Now calculate b: b = (-4/3)(3) + 3

b = -4 + 3 b = 1

You now get the final equation: y = (-4/3)x + 1 now that you have the base.

This line will intersect point (3,-3) and be perpendicular to the line y = (3/4)x + 5.

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Complete question:

write an equation passing through the point that is perpendicular to(3,-3); y= 3/4 x+5

The solution to the initial value problem is [tex]y = 4e^{(5x^{10})[/tex]. The domain of the function is all real numbers.

Ordinary differential equations of the first order only take into account the dependent variable y's first derivative with regard to the independent variable x. They could be written as follows:

f(x,y) = dy/dx

where the supplied function of both x and y is f(x,y). There are numerous methods for solving first-order ordinary differential equations, which are crucial in many branches of science and engineering. One such method is variable separation. Other methods include Bernoulli equations, integrating components, and precise equations.

The given differential function is:

[tex]dy/dx = 10x{^9}y[/tex]

Separating the variables we have:

dy/y = 10x^9 dx

Now, integrating on both sides:

[tex]]int dy/y = \int 10x^9 dx\\ln (y) = 5x^{10} + C[/tex]

Solving for y:

[tex]y = ke^{(5x^{10})[/tex]

Now, for the initial values y = 4 and x = 0 we have:

[tex]4 = ke^{(0)}[/tex]

k = 4

Hence, the solution to the initial value problem is [tex]y = 4e^{(5x^{10})}[/tex].

The domain of the function is all real numbers.

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The function after each transformation is given as follows:

1. Reflected across the x-axis: f(x) = -|x + 3| + 7.

2. Translated left 4 units: f(x) = |x + 7| - 7.

3. Translated down 3 units: f(x) = |x + 3| - 10

The function for this problem is defined as follows:

f(x) = |x + 3| - 7.

When the function is reflected across the x-axis, we have that the entire function is multiplied by -1, hence:

f(x) = -(|x + 3| - 7)

f(x) = -|x + 3| + 7.

When the function is translated left 4 units, we have that x -> x + 4, hence:

f(x) = |x + 4 + 3| - 7

f(x) = |x + 7| - 7.

When the function is translated down 3 units, we have that f(x) -> f(x) - 3, hence:

f(x) = |x + 3| - 7 - 3

f(x) = |x + 3| - 10

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The distance between control room to airplane is 41027.5 feet.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here This distance (d) from tower will be the hypotenuse of a right triangle.

The altitude is the side opposite the angle at the tower

The tower is 200' high, therefore, the altitude above the tower.

=> 5200 - 200 = 5000 feet.

Now using sine ratio then,

=> Sin 7° = AC/BC

=> BC = AC/sin 7°

=> BC = 5000/sin 7°

=> BC = d = 41027.5 feet.

Hence the distance between control room to airplane is 41027.5 feet.

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The probability that you lose both times in the instant lottery is 0.81.

In order to find the probability of losing both times in the instant lottery, we can use the following steps:
Determine the probability of losing once:

Since the probability of winning is 0.1, the probability of losing is 1 - 0.1 = 0.9.
Calculate the probability of losing twice:

Since the outcomes are independent, we can multiply the probabilities of losing each time.

So, the probability of losing both times is 0.9 * 0.9.
Calculate the final result: 0.9 * 0.9 = 0.81.

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Answer:The term used for the $400 difference in Alex and Alecia's tax liability is known as the marriage penalty. Option C

The marriage penalty refers to the situation in which a married couple pays more taxes than they would if they were both single and filing separately. This penalty arises due to the progressive tax system in which the tax rate increases as the income increases. When two individuals with similar income levels get married and file jointly, their combined income puts them in a higher tax bracket, resulting in a higher tax liability.

In this case, Alex and Alecia's joint tax liability is $9,300, which is higher than the sum of their individual tax liabilities ($3,900 + $5,000 = $8,900). Therefore, they are paying an extra $400 due to the marriage penalty. This penalty can be significant for couples with similar incomes, as it can impact their financial planning and budgeting. However, there are also cases in which couples may benefit from the marriage tax advantage, such as when one spouse earns significantly less than the other.

Overall, it is essential for couples to understand their tax liability and to explore different filing options to determine the most advantageous one for their particular situation. Therefore option C is correct.

Step-by-step explanation:

Answer:

neither

$0

No

Step-by-step explanation:

The radius of the lid would be 3. 5 cm.

To estimate the radius of the lid, we must first determine the circumference of the jar, which is equal to the jar's perimeter. The specified circumference is 21.98 cm.

The circumference is:

C = 2πr

We can solve for circumference as:

21. 98 = 2 πr

r = 21. 98 / ( 2 π )

r = 21. 98 / (2 x 3. 1416 )

r = 21. 98 / 6. 2832

r = 3. 5 cm

In conclusion, the radius of the lid is approximately 3.5 cm.

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Answer:

I put the equation on math-way and it gave me this:

Answer:

Starting at (0, 1), go up 4 units, then right 3 units. You will end at (3, 5). Plot that point, and then draw a line that goes through the two points.