Consider the equation: x² + 10x + 22 = 13 1) Rewrite the equation by completing the square. Your equation should look like (x + c)2 = dor (x - c)² = d. 2) What are the solutions to the equation? Choose 1 answer: A x=5±4 x = -5±4 x = 5±16 x = -5±16​

Answer:

6^2 + 4(1/2)(6)(9) = 36 + 108 =

144 square meters

If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

The conversion factor that states [tex]1[/tex] gramme is about equivalent to [tex]0.035[/tex]ounces can be used to convert grammes to ounces.

we may multiply  [tex]5[/tex] by  [tex]0.035[/tex] to convert [tex]5[/tex] grammes to ounces:

[tex]5 grams \times 0.035 \ oz/gram = 0.175[/tex] ounces

It's vital to remember that the ratio of 1 gramme to  [tex]0.035[/tex] ounces is merely an estimate; the precise ratio is 1 gramme to [tex]0.03527396195[/tex] ounces.

However, utilizing the streamlined conversion factor of [tex]1[/tex] gramme to [tex]0.035[/tex] ounces is accurate enough for the majority of routine uses.

Therefore,If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

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Answer:

b

Step-by-step explanation:

Hence, it will take 2.6 hours for the two trains to be 520 miles apart.

Distance is a numerical or occasionally  qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

In everyday use and in kinematics, the speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity..

The two trains are moving  away from each other,

so we can  add their speeds to get their relative speed:

relative speed = 95 mph + 105 mph = 200 mph

Now ,we determine  the time it takes for the trains to be 520 miles apart,

so we can use the formula:

distance = speed × time

let t be the time  it takes for the trains to be 520 miles apart.

Then we get,

520 = 200 × t

Solving for t, we get:

t = [tex]\frac{520}{200}[/tex]

t = 2.6 hours

Therefore, it will take 2.6 hours for the two trains to be 520 miles apart.

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B

Step-by-step explanation:

Standard deviation is the best method for comparing the spread of frequency distributions for two groups, as it provides an accurate and sensitive measure of variability.

To compare the spread of the frequency distributions for two groups, we can use the measure of variability called the standard deviation. The standard deviation provides a measure of how much the data points are spread out around the mean.

A smaller standard deviation indicates that the data points are clustered closely around the mean, whereas a larger standard deviation indicates that the data points are more spread out from the mean.

The reason why standard deviation is a good measure of spread is that it is sensitive to the distance between data points and the mean. Therefore, it provides an accurate measure of how much the data is spread out, regardless of the shape of the distribution.

To calculate the standard deviation, we first need to calculate the mean of each group, and then the difference between each data point and the mean, squared.

We then take the average of these squared differences and take the square root to get the standard deviation.

For example, suppose we have two groups of test scores:

Group A: 75, 80, 85, 90, 95

Group B: 60, 70, 80, 90, 100

To calculate the standard deviation for Group A, we first calculate the mean:

(75 + 80 + 85 + 90 + 95) / 5 = 85

Then we calculate the difference between each data point and the mean, squared:

(75 - 85)² = 100

(80 - 85)² = 25

(85 - 85)² = 0

(90 - 85)² = 25

(95 - 85)² = 100

Next, we take the average of these squared differences:

(100 + 25 + 0 + 25 + 100) / 5 = 50

Finally, we take the square root of this average:

√(50) = 7.07

Therefore, the standard deviation for Group A is 7.07. We can repeat these steps for Group B and compare the two standard deviations to determine which group has a larger spread.

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What will likely happen to the price of the toy after it lost popularity is that the price would go down, because demand decreased. That is option D.

The effect of decrease in the popularity of a product affects both it's demand and the cost price.

Since the product is less needed by the consumers and population at large the manufacturer would adjust the cost price to enhance its sales output at the end of each business month.

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Answer: $63.40

Step-by-step explanation:

She starts out with $317  but she will only get 80%  which means she will lose 20%

100%-80%=20%

take 20% of 317

.2 x 317    convert 20% to decimal by moving decimal twice and multiply

=63.4

She will lose $63.40

Reason:

If she withdraws early, she can only withdraw 80% of what she put in. She takes a 20% penalty.

20% of 317 = 0.20*317 = 63.40 dollars is how much she loses.

Put another way:

She is able to withdraw 0.80*317 = 253.60 dollars if doing so early. She lost 317-253.60 = 63.40 dollars

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]

99.57 units is the measurement of the hypotenuse for the given triangle.

In this case, the legs of the triangle are 7x+6 and 5x, so we have:

a = 7x+6

b = 5x

Substituting x = 11, we get:

a = 7(11) + 6 = 83

b = 5(11) = 55

Now we can use the Pythagorean theorem to find the length of the hypotenuse:

[tex]c^2 = a^2 + b^2\\c^2 = 83^2 + 55^2\\c^2 = 6889 + 3025\\c^2 = 9914[/tex]

Taking the square root of both sides, we get:

c = √9914 ≈ 99.57

Therefore, the length of the hypotenuse of the triangle is approximately 99.57 units.

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The simplified form of the given expression, can be found to be A. x² + 7x + 5.

Simplified expressions are algebraic expressions that have been reduced to their simplest form by applying the rules of arithmetic and algebra.

To simplify the expression, we add the corresponding terms from both expressions:

(-3x² + 2x - 4) + (4x² + 5x + 9)

Combine the x² terms: -3x² + 4x² = 1x² (or simply x²)

Combine the x terms: 2x + 5x = 7x

Combine the constants: -4 + 9 = 5

So, the simplified expression is:

x² + 7x + 5

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Answer:

blank is 4

Step-by-step explanation:

We can set up the equation:

[tex]\frac{1}{8} *x = \frac{1}{2}[/tex]

To solve, multiply both sides by 8.

[tex]\frac{1}{2}*8 = 4[/tex]

This checks out with the other statement.

To find A's best response to B choosing L in normal form game, we can compare the payoffs for A choosing H and L when B chooses L.

If A chooses H and B chooses L, then A's payoff is 0 and B's payoff is 6.

If A chooses L and B chooses L, then A's payoff is 3 and B's payoff is 3.

Comparing the payoffs, we see that A gets a higher payoff if he chooses H when B chooses L. Therefore, A's best response to B choosing L is H.

To find B's best response to A choosing L, we can compare the payoffs for B choosing H and L when A chooses L.

If A chooses L and B chooses H, then A's payoff is 9 and B's payoff is 4.

If A chooses L and B chooses L, then A's payoff is 3 and B's payoff is 3.

Comparing the payoffs, we see that B gets a higher payoff if he chooses L when A chooses L. Therefore, B's best response to A choosing L is L.

So, the answer is (c) L;H. A's best response to B choosing L is H, and B's best response to A choosing L is L.

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If the researcher is interested in testing if a particular value is either greater or smaller than the hypothesized value, then a one-tailed test is appropriate

The decision of whether to use a one-tailed test or a two-tailed test when testing hypotheses depends on the nature of the situation and what the researcher is trying to demonstrate. . If the researcher is interested in testing if a particular value is simply different from the hypothesized value, then a two-tailed test is appropriate. The level of significance of the test is also an important consideration, but it is not the primary determinant of whether to use a one-tailed or two-tailed test.

what is demonstrate?

To demonstrate means to show or prove something convincingly with evidence or argument. It is a way of providing support for a claim or idea.

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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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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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The critical z-value for a 98% confidence level is 2.33.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

Statistics plays a significant role in various fields, including business, economics, social sciences, medicine, engineering, and many others.

To find the critical z value for a 98% confidence level, we need to look up the z-value associated with an area of 0.01 in the upper tail of the standard normal distribution table (since 98% of the area lies within the confidence interval, leaving 2% in the tails).

Using a standard normal distribution table, we can find that the z-value that corresponds to an area of 0.01 in the upper tail is approximately 2.33.

Therefore, the critical z-value for a 98% confidence level is 2.33.

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Answer:

2l + 2w = 24, so l + w = 12

A(l) = l(12 - l)

The equation r · sin θ = 10 in rectangular coordinates is equal to y = 10.

Herein we find the representation of a equation in polar coordinates, whose form in rectangular coordinates. This can be done by using the following definitions:

cos θ = x / r

sin θ = y / r

Where:

Then, the equation in polar coordinates is:

r · sin θ = 10

y = 10

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Answer: 3x²-2x+5=0

You subtract the 2x and add 9 from both sides to get 3x²-2x+9=0

Answer:

3x^2−2x+5=0

Step-by-step explanation:

3x^2-4=2x-9

first you gotta add 9 to both sides

3x^2+5=2x

then you gotta subtract 2x from both sides

3x^2-2x+5=0

-SpoOky

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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Neither of the segments is the perpendicular bisector of the other.

To determine which segment is the perpendicular bisector of the other, we need to find the equations of the lines containing each segment and then check if one of the lines is perpendicular to the other and passes through the midpoint of the other segment.

Let's start by finding the midpoint of segment AT. The coordinates of A and T are not given, but we don't actually need them to find the midpoint.

So, the midpoint M of segment AT is:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2)

We don't know the actual values of AT_x1, AT_x2, AT_y1, and AT_y2, but we can find their expressions in terms of x using the segment lengths and the coordinates of the endpoints. We have:

AT_x2 - AT_x1 = BT_x2 - AT_x1 = (x + 5) - (2x + 3) = -x + 2

AT_y2 - AT_y1 = BT_y2 - AT_y1 = (BT - AT) = (x + 5) - (2x + 3) = x + 2

Therefore,

AT_x1 = AT_x2 + x - 2

AT_y1 = AT_y2 - x - 2

Now, we can substitute x=2 and the expressions for AT_x1 and AT_y1 into the midpoint formula to find the coordinates of M:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2) = ((AT_x2 + 2 - AT_x2)/2, (AT_y2 - 2 - AT_y2)/2) = (1, -1)

So, the midpoint of segment AT is M(1, -1).

Next, let's find the equations of the lines containing segments AT and DT. We can use the point-slope form of the equation of a line, which states that the equation of a line passing through a point (x1, y1) with slope m is y - y1 = m(x - x1).

For segment AT, we have:

m_AT = (AT_y2 - AT_y1)/(AT_x2 - AT_x1) = (x + 2)/(x - 1)

Let's substitute x=2 to find the slope of the line containing segment AT:

m_AT = (2 + 2)/(2 - 1) = 4

So, the equation of the line containing segment AT is:

y - AT_y1 = m_AT(x - AT_x1)

y - (22 + 3) = 4(x - 22 - 1)

y - 7 = 4(x - 5)

y = 4x - 13

For segment DT, we have:

m_DT = tan(m∠ATD) = tan(41x + 8)

Let's substitute x=2 and simplify:

m_DT = tan(82 + 8) = tan(90) = undefined

This means that the line containing segment DT is vertical and its equation is x = DT_x1 = 4*2 + 1 = 9.

Now, we need to check if one of these lines is perpendicular to the other and passes through the midpoint of the other segment.

First, let's check if the line containing segment AT is perpendicular to the line containing segment DT.  We have:

m_AT * m_DT = 4 * undefined = undefined

Since undefined is not equal to -1, the lines are not perpendicular, and we can rule out the possibility that the line containing segment AT is the perpendicular bisector of segment DT.

Next, let's check if the line containing segment DT is perpendicular to the line containing segment AT. We have:

m_AT = 4

So, the slope of the line perpendicular to the line containing segment AT is -1/4. We can use the point-slope form of the equation of a line again:

y - M_y = -1/4(x - M_x)

y - (-1) = -1/4(x - 1)

y + 1 = -1/4x + 1/4

y = -1/4x + 3/4

Now, we need to check if this line passes through point D, an endpoint of segment DT. We can substitute the coordinates of D into the equation of the line and check if the equation holds true:

DT_y1 = 4*2 + 1 = 9

DT_x1 = 9

9 = -1/4*9 + 3/4

9 = -9/4 + 3/4

9 = -6/4

This is not true, so the line containing segment DT does not pass through point D. Therefore, we can conclude that the line containing segment DT is not the perpendicular bisector of segment AT.

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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 reasonable estimate of the median home cost in the US in 2025 is  $340,000

To assess the middle domestic taking a toll within the US in 2025, ready to utilize the verifiable drift and expect that the relationship between the middle domestic fetched and time (measured in a long time since 1975) is straight.

Let`s begin with calculating the rate of increment in median domestic fetched per year utilizing the information from 1975 to 2005. Ready to utilize the equation for the slant of a direct relapse line:

slant(slope) = (y2 - y1) / (x2 - x1)

where

y1 and y2 are the middle domestic costs in 1975 and 2005,

separately, and x1 and x2 are comparing a long time (0 and 30).

incline = ($240,000 - $40,000) / (30 - 0) = $6,000

This implies that the middle domestic taken a toll expanded by a normal of $6,000 per year amid this period.

Presently, ready to utilize this rate of increment to appraise the middle domestic taken a toll in 2025, which is 50 long times after 1975.

The year 2025 will be 50 a long time after 1975, so the number of a long time since 1975 will be x = 50. Utilizing the incline we fair calculated, able to assess the middle domestic fetched in 2025 as takes after 

y = y1 + slant(slope) * x = $40,000 + $6,000 * 50 = $340,000

Therefore, a sensible assessment of the middle domestic taking a toll within the US in 2025, based on the presumption that the slant watched from 1975 to 2005 proceeds, is $340,000. 

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Answer:

1) 18 Red balls

2) 12 blue balls

3) [tex]\frac{5}{3}[/tex] green balls to red balls

Step-by-step explanation:

R  B  G

3:2:5

3+2+5 = 10

60/10 = 6

to find the number of red balls simply do

3 * 6 = 18

to find the number of blue balls do

2 * 6 = 12

to find the number of green balls do

5 *6 = 30

the ratio of green/red same as the original

5/3  

The solution to the given problem of the unitary method comes out to be Plan A and Plan B thus lasting for a total of 1.25 hours each.

Finish the project using the tried-and-true basic methodology, the actual variables, and any pertinent knowledge you gain from the broad and specific questions. In response, customers might be given another opportunity to sample the expression the products. We'll miss out on important breakthroughs in programming comprehension if these changes don't take place.

Here,

Let's say that Plan A's duration is "a" hours and Plan B's duration is "b" hours.

=> Equation 1: 6a + 2b = 10.

=>  Equation 2: 3a + 5b = 10.

To get rid of "a," multiply Equation 1 by 3 and Equation 2 by 6 and you get:

=> Equation 3: 18a + 6b = 30

=> Equation 4: 18a + 30b = 60

Equation 3 minus Equation 4 results in:

=>  24b = 30

When we multiply both sides by 24, we get:

=> b=30/24=5/4=1.25 hours.

The value of "b" can now be reinserted into Equation 3 to find "a":

=> 18a + 6(1.25) = 30

=> 18a + 7.5 = 30

=> 18a = 30 - 7.5

=> 18a = 22.5

When we multiply both sides by 18, we get:

=> if a = 22.5/18 then 1.25 hours.

Plan A and Plan B thus last for a total of 1.25 hours each.

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The surface area of the rectangle prism is 96cm²

A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is expressed as;

SA = 2B +pH

where B is the base area and p is the perimeter of the base and h is the height of the prism.

Base area = 4× 2 = 8cm²

perimeter of the base = 2(4+2) = 2× 8 = 16cm²

height = 5cm

therefore the surface area of the prism

= 2×8 + 5×16

= 16+80

= 96cm²

therefore the surface area of the prism is 96cm²

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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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Answer:

607,532

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