If the quadratic equation has two rational roots,then the discriminant is_____and a perfect square

There would be about 12 pieces of fruit in the bag.

Answer:

t = 0 , d = 0

t = 2, d = 22

t= 4, d = 44

t = 6, d = 66

Step-by-step explanation:

Here, given the equation that relates the time in seconds to the distance in feet, we want to complete the given table

From the equation, we have that d = 11t

This mean that by multiplying the time by 11, we get the distance

Thus, we have that ;

when t = 0

d = 11 * 0 = 0

when t = 2

d = 11 * 2 = 22 ft

when t = 4

d = 11 * 4 = 44 ft

when t = 6

d = 11 * 6 = 66 ft

Given the equation that models the proportional relationship, the missing values in the table are: 0, 22, 44, and 66.

Given:

d = 11t

Find the corresponding values of d by plugging in the given values of t:

When t = 0,

d = 11(0) = 0

When t = 2,

d = 11(2) = 22

When t = 4,

d = 11(4) = 44

When t = 6,

d = 11(4) = 66.

Therefore, given the equation that models the proportional relationship, the missing values in the table are: 0, 22, 44, and 66.

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Answer:

A)1/2

Step-by-step explanation:

To find the determinant of a matrix using row reduction to echelon form, you can follow these steps:

1. Start with the given matrix.

2. Apply row operations to convert the matrix into echelon form. Row operations include multiplying a row by a nonzero scalar, adding a multiple of one row to another, and swapping two rows.

3. Continue performing row operations until you reach the echelon form, where all leading coefficients (the leftmost nonzero entry in each row) are 1 and the entries below leading coefficients are all zeros.

4. Once you have the matrix in echelon form, the determinant can be calculated by multiplying the leading coefficients of each row.

5. If you perform any row swaps during the row reduction process, keep track of the number of swaps. If the number of swaps is odd, multiply the determinant by -1.

Let's look at an example to illustrate these steps. Suppose we have the following 3x3 matrix:

| 2  1  3 |
| 1 -2 -4 |
| 3  0  1 |

Step 1: Start with the given matrix.

Step 2: Apply row operations to convert the matrix into echelon form.

First, we can multiply the first row by -1/2 and add it to the second row, resulting in:

| 2   1   3  |
| 0  -5/2 -5/2|
| 3   0    1  |

Next, multiply the first row by -3/2 and add it to the third row, giving us:

| 2   1   3  |
| 0  -5/2 -5/2|
| 0  -3/2 -8/2|

Finally, multiply the second row by -2/5 to get a leading coefficient of 1:

| 2   1   3  |
| 0   1    1 |
| 0  -3/2 -8/2|

Step 3: The matrix is now in echelon form.

Step 4: Calculate the determinant by multiplying the leading coefficients of each row:

2 * 1 * (-8/2) = -8

Step 5: Since no row swaps were performed, we don't need to multiply the determinant by -1.

Therefore, the determinant of the given matrix is -8.

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Inverse function of f(x)=5x+2 and determine its domain, range, and whether it is a function. Step 1: Start by replacing f(x) with

Yes, f⁻¹ is a function because each input x has a unique output (y = (x - 2)/5).

y: y = 5x + 2

Step 2: Swap x and y:
  x = 5y + 2

Step 3: Solve for y:
  x - 2 = 5y
  (x - 2)/5 = y
  y = (x - 2)/5

Step 4: Replace y with f⁻¹(x):
  f⁻¹(x) = (x - 2)/5

Step 5: Determine the domain and range of f:
  The domain of f is all real numbers, as there are no restrictions on the values of x.

  To find the range, we consider that f(x) is a linear function with a positive slope of 5. This means that the range is also all real numbers.

Step 6: Determine the domain and range of f⁻¹:
  The domain of f⁻¹ is also all real numbers, as there are no restrictions on the values of x.

  The range of f⁻¹ is also all real numbers, as the function f⁻¹(x) is a linear function.

Step 7: Determine if f⁻¹ is a function:
  Yes, f⁻¹ is a function because each input x has a unique output (y = (x - 2)/5).

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Answer:

x - 10 ≥ 30

Step-by-step explanation:

I'm 99.8% sure

It says 10 less than a number so that means subtract 10 from a number

Then it says minimum of 30 so that means the number has to be 30 or more so that's why I use the more than of equal to sign.

Hope this helps!

Answer:

$94.05

Step-by-step explanation:

Original price of jeans=$95

Discount=10%

New price=(100% - 10%) of $95

=90% × 95

=90/100 × 95

=0.9 × 95

=$85.5

Sales tax of 10%

10% of the new price

=10/100 × 85.5

=0.1 × 85.5

=$8.55

Sales tax =$8.55

Total amount paid for the jeans= sales tax + new tax

=$8.55 + $85.5

=$94.05

The price of each bagel sold when 312 bagels are sold and $280.80 earned  is $ 0.9.

One of the four basic mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups.

The number of bagels sold = 312

The total money earned by selling 312 bagels = $ 280 . 80

The price for each bagel,

\(=\frac{total money earned}{number of bagels sold} \\\\=\frac{280.80}{312} \\\\=$0.9\)

So, the price of each bagel sold is $ 0.9.

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DM is congruent to line CM because CDM is congruent to triangle CBM using the SAS congruence criteria for triangles.

Draw a diagram of the rectangle ABCD with M as the midpoint of AB. Draw lines CM and DM ( refer to the attached image). Since AB is a line segment, we know that AM is congruent to MB (because M is the midpoint of AB). Since ABCD is a rectangle, we know that AB is parallel to CD, and AD is parallel to BC. Thus, we have two pairs of parallel lines: AB and CD, and AD and BC.

Using the fact that opposite sides of a rectangle are congruent, we have CD = AB. Now, we have a pair of congruent sides (DM and CM) that are opposite each other in triangle CDM and CBM respectively. We also have another pair of congruent sides (CD and AB) that are opposite each other in both triangles. Finally, we know that the angle CMD is congruent to the angle CMB because they are vertical angles. By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle CDM is congruent to triangle CBM.

Therefore, line DM is congruent to line CM by SAS congruence criteria.

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The median number of hours spent practicing per week during the nine consecutive weeks is the middle value when the hours are arranged in ascending order.

To find the median, we first need to arrange the recorded number of hours spent practicing per week in ascending order. Let's assume the recorded hours are as follows: 2, 3, 4, 5, 5, 6, 7, 8, 9.

There are a total of nine recorded hours. Since the number of hours is odd, the median will be the middle value. In this case, the middle value is the fifth number, which is 5. Therefore, the median number of hours spent practicing per week during the nine consecutive weeks is 5.

The median is a measure of central tendency that represents the middle value in a set of data. It is a useful measure for finding a typical value in a distribution. In this case, the median gives us an idea of the "typical" number of hours spent practicing per week during the nine-week period.

By arranging the hours in ascending order, we can easily identify the middle value as the median. In situations where there is an even number of data points, the median would be the average of the two middle values.

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Let's solve the equation:

Therefore, the solutions of the equation are x=1 and x=-5

The probability that exactly one box is empty is n × (n - 1)^(n - 2).

In a given scenario, we have n balls and n boxes, with each box being equally likely to contain a ball. We need to find the probability that just one box remains empty. Therefore, there are two cases to consider:

Case 1: There is one box empty and the other n - 1 boxes contain one ball each. We have n choices for the empty box, and once that box is empty, we have n - 1 balls left, which we need to distribute to n - 1 boxes. So, the probability of Case 1 occurring is: P1 = n × (n - 1)^(n - 1)

Case 2: There are two boxes with more than one ball each and one box with no ball. We can choose the empty box in n ways, and then we need to distribute n balls over the remaining n - 1 boxes. Since there are two boxes with more than one ball each, there are (n - 1) choices for each ball, resulting in (n - 1)^n-2 ways to distribute the balls. Thus, the probability of Case 2 is: P2 = n × (n - 1)^n-2. Using the principle of inclusion-exclusion, the probability of exactly one box being empty is given by: P = P1 - P2 = n × (n - 1)^(n - 1) - n × (n - 1)^n-2 = n × (n - 1)^(n - 2) × ((n - 1) - (n - 2)) = n × (n - 1)^(n - 2)

Therefore, the probability that exactly one box is empty is n × (n - 1)^(n - 2).

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Using simple interest, it is found that Katelyn's brother borrowed 15,889 for school.

The amount of interest after t years in simple interest is modeled by:

\(I(t) = Prt\)

In which:

In this problem:

Then:

\(I(t) = Prt\)

\(5720 = P(0.06)(6)\)

\(0.36P = 5720\)

\(P = \frac{5720}{0.36}\)

\(P = 15889\)

Katelyn's brother borrowed 15,889 for school.

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Answer:

ok the answer is 10

Step-by-step explanation:

Just put 10 lol

The appropriate null hypothesis (H0) would be that the proportion of students who support sports passes being included in tuition is equal to or less than 50%. The alternative hypothesis (Ha) would be that the proportion is greater than 50%.

In hypothesis testing, the null hypothesis represents the default assumption, while the alternative hypothesis challenges this assumption. In this case, the null hypothesis (H0) would state that the proportion of students supporting sports passes being included in tuition is 50% or less (i.e., not more than half). The alternative hypothesis (Ha) would assert that the proportion is greater than 50%.

To express this formally, we can define the null and alternative hypotheses as follows:

H0: p ≤ 0.5

Ha: p > 0.5

Here, 'p' represents the true population proportion of students who support sports passes being included in tuition. The null hypothesis assumes that 'p' is 0.5 or less, while the alternative hypothesis suggests that 'p' is greater than 0.5.

By conducting hypothesis testing using the collected sample data, we can determine whether there is sufficient evidence to reject the null hypothesis and support the claim that more than half of the students support the inclusion of sports passes in tuition.

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Answer: D. \(6^{30}\)

Step-by-step explanation:

Using exponent rules an exponent to the power of a number will multiply by each other.

So the -4 and -9 will multiply.

The 6 in the numerator will now have a positive exponent of 36.

\(\frac{6^{36}}{6^6}\)

Now we can divide and when we do so the exponents will subtract from each other.

So 36 - 6 = 30

And the base of 6 does not change.

The simplified form is \(6^{30}\)

Answer: D.

Step-by-step explanation:

Using exponent rules an exponent to the power of a number will multiply by each other.

So the -4 and -9 will multiply.

The 6 in the numerator will now have a positive exponent of 36.

Now we can divide and when we do so the exponents will subtract from each other.

So 36 - 6 = 30

And the base of 6 does not change.

The simplified form is  

\(6^{30}\)

Answer:

428

160

12.7

Step-by-step explanation:

So I'm pretty sure all it's asking you do is divide the product (number on the right) by the number on the left!

So 42.8/\(\frac{1}{10}\)=428

1600/10=160

1.27/\(\frac{1}{10}\)=127

Answer:

175

Step-by-step explanation:

hey! so it's basically an "estimate" meaning that you can round all the measurements up to the nearest whole number. and since finding the prism's volume is l*h*w divided by 2, i did 7*5*10 and got 350. half of 350 is 175 which is the volume of the prism :)

Answer:

175

Step-by-step explanation:

the formula of triangular prism is

v = 1÷2( b×h×l)

base (b) =5.1cm

height( h) = 6.9

length ( l) = 9.9

v =1÷2 ( 5.1 × 6.9× 9.9 )

v = 174.19 cm^3

so th closest will be 175cm^3

The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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The rate of return if the price of Telecom stock goes up by 10% during the next year is 12%.

The rate of return (RoR) is a rate of return that calculates the net profit or loss of an investment over a certain period of time, and is expressed as a percentage. RoR is an indicator that can be useful to see the level of efficiency in an investment. When the RoR is positive, it means that the investment is making a profit.

Conversely, when the RoR is negative, it reflects a loss in investment. The higher the percentage RoR value, the higher the level of investment you can invest. For example, if the investment is IDR 1,000,000 and has a rate of return of 22%, then the growth rate is 22%.

Based on the question above,

Buy 200 shares of Telekom stock at $50 for $10,000.

The value of these shares increases by 10% or $1,000.

Interest expense = 0.08 x 5,000 = $400

Return values are:

(price increase - interest expense) / borrowed assets

= $1000 - $400 / $5000

= 0.12 = 12%

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From the circle it can be observed that measure of arc PRT is more than 180 degree. So arc PRT is a major arc.

Determine the measure of arc PRT.

Thus measure of arc PRT is 270 degree.

If we are interested in a larger class size Riverside School is a better choice because its mean and median class sizes are both larger than those of Sky View School.

The measures of center need to find the mean and median for each school.

For Sky View School:

Mean = (210 + 112 + 913 + 114) / 15 = 10.2

Median = (5+5)/2 = 5

For Riverside School:

Mean = (220 + 321 + 522 + 723 + 624 + 425 + 226 + 027 + 028 + 129) / 30 = 23

Median = (6+7)/2 = 6.5

The mean class size at Sky View School is 10.2 and at Riverside School is 23.

The median class size at Sky View School is 5 and at Riverside School is 6.5.

The measures of variability need to find the range interquartile range (IQR) and standard deviation for each school.

For Sky View School:

Range = 13-5 = 8

Q1 = 10, Q3 = 12

IQR = Q3 - Q1 = 2

Standard deviation = 2.37

For Riverside School:

Range = 29-20 = 9

Q1 = 22, Q3 = 25

IQR = Q3 - Q1 = 3

Standard deviation = 3.32

The range of class sizes at Sky View School is 8 and at Riverside School is 9.

The IQR of class sizes at Sky View School is 2 and at Riverside School is 3.

The standard deviation of class sizes at Sky View School is 2.37 and at Riverside School is 3.32.

Riverside School has a larger maximum class size (29) compared to Sky View School (13).

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Answer:

simply divide the numerator and denominator by 4 (the GCF). So, 1232 = 12÷432÷4 = 38. Thus, 1232 is equivalent to 38 in the reduced form. (*) The factors are numbers that multiply each other to get another number.Step-by-step explanation:

Answer:

3:8

Step-by-step explanation:

We can simplify the ratio 12 : 32 by dividing both terms by the greatest common factor (GCF).

The GCF of 12 and 32 is 4.

Divide both terms by 4.

12 ÷ 4 = 3

32 ÷ 4 = 8

Therefore:

12 : 32 = 3 : 8

I hope this helped, If this is wrong then I'm sorry but I think this is accurate.

Jim and Lillian are painting a wall that is 15 ft wide and 9 feet tall and they will need to buy $ 135x of paint to paint the whole wall, where "x" is the cost of painting per square feet of the wall.

To solve this question, we will move ahead with a very direct approach of problem solving which is, step-by-step formulation.

First, we will calculate the area of the wall to be painted by using the formula to calculate the area of a rectangle which goes as

\((l*b)\) sq. feet where, "l" is the length or height of the rectangle and "b" is the breadth or width of it.

Then, we will just multiply the calculated area with the rate of painting per unit.

Here, as per data provided in the question statement, the wall to be painted is 15 ft wide and 9 feet tall, i.e., (l = 15) and (b = 9).

Therefore, area of the wall = \((15*9)=135\) square feet.

And since, no rate of painting is provided, let us assume that the rate of painting per square feet is $ x, then, amount of paint to be purchased to paint the wall will be \((135*x)=$135x\) Dollars.

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Answer:

1/2

Step-by-step explanation:

Out of a total 12 donuts, 6 of them are maple. Assuming this ratio stays constant, the experimental probability that the next one sold is a maple donut is 6/12=1/2. Hope this helps!

Answer:

P(maple donut) = 0.5

Step-by-step explanation:

If they sold 12 donuts, of which 6 of them were Maple Donuts.

The experimental probability of donuts sold that were maple donuts is:

\(\frac{6}{12}=\frac{1}{2}=0.5\)

Therefore donuts sold in the future, would follow this probability, so our answer is 0.5.

As we can conclude from the graphical method that this system has no common intersection point they have no solution.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given system of equations are x + 2y = 4, 3x + 6y = 6, 3x - y = 5 and

6x - 2y = 10.

The graphical representation of these equations are attached in the image below.

As we can observe , 3x - y = 5(green line)  and 6x - 2y = 10(purple line) are coinciding with each other so they have infinite no. of solutions.

x + 2y = 4(red) and 3x + 6y = 6(blue) are parallel to each other and hence have no solution.

And in together all these 4 lines have no common intersection point so they have no solution.

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Answer:

x= -7-11

x=-18

Step-by-step explanation:

We must find the sum of the polynomials:

The sum of the polynomials give:

Answer

By using the concept of statistics mean of sample distribution is 260 and standard deviation is 4

The practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample. is called as statistics.

More Importantly ,Statistics is used to do calculations of huge data distributed in some ways.

We have mean of infinite population. Mean of random sample will be also 260.

Now talking about standard error of the mean ,

we know very well that standard error of mean=standard deviation/\(\sqrt{x}\)

where x is size

We know that sample size is 16

Therefore standard error of mean is =16/\(\sqrt{16}\)=16/4=4

Hence mean of random sample is 260 and standard error of mean is 4

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