A football team gains 8 yards in one play, then loses 5 yards in the next. What is the team’s total yardage for the two plays?

The factored form of the cubic equation x³ + 27 is equal to (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2). The roots of the cubic equation are - 3, 3 / 2 + i 3√3 / 2 and 3 / 2 - i 3√3 / 2.

In this problem we find a cubic equation of the form x³ + a³, whose factor form can be found by using algebra properties:

f(x) = x³ + 27

f(x) = (x + 3) · (x² - 3 · x + 9)

f(x) = (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2)

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Answer:

length of the opposite leg divided by the hypotenuse

Step-by-step explanation:

Answer:

1000 times greater.

Step-by-step explanation:

10^9 / 10*6

= 10^(9-6)

= 10^3

= 1000.

Answer:

just took the test answer is C

Step-by-step explanation:

The sample size is needed so that the 95% confidence interval will have a margin of error of no more than 3% is 1067.11

In medical research, it is essential to determine the effectiveness of a drug on a certain disease or disorder. Scientists often use statistical methods to estimate the proportion of patients who would benefit from taking the drug. In this case, the scientists want to estimate the proportion of patients who would benefit from a new drug for a certain blood disorder.

To estimate the proportion of patients who would benefit from the drug, the scientists need to create a confidence interval. A confidence interval is a range of values that is likely to contain the true value of the proportion of patients who would benefit from the drug. The margin of error is the maximum amount by which the confidence interval is expected to differ from the true value of the proportion.

To determine the sample size needed to create a confidence interval with a margin of error of no more than 3%, the scientists need to use a formula. The formula is:

n = (Z² * p * q) / E²

Where:

n = sample size

Z = the Z-score for the desired confidence level (in this case, a 95% confidence interval corresponds to a Z-score of 1.96)

p = the proportion of patients who would benefit from the drug (unknown)

q = 1 - p

E = the desired margin of error (in this case, 0.03 or 3%)

The scientists know that they want a margin of error of no more than 3%, which means that E = 0.03. They also know that they want a 95% confidence interval, which corresponds to a Z-score of 1.96. The only unknown in the formula is the proportion of patients who would benefit from the drug (p).

The scientists estimate that about half of all people with the blood disorder would benefit from the drug. Therefore, they assume that p = 0.5. They plug in the values into the formula:

n = (1.96² x 0.5 x 0.5) / 0.03²

n = 1067.11

They round up to the nearest whole number and determine that they need a sample size of at least 1068 patients to create a 95% confidence interval with a margin of error of no more than 3%.

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Answer:

12

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

So, Leena eats 1/8 of the bread first.

Now, she gave 1/6 of the bread to EACH of her 3 friends.

So you will need to do 1/6*3, which is 3/6=1/2.

Now you want to do 1/8+1/2 = 1/8+4/8 = 5/8.

This means 5/8 of the bread is gone.

Now you will need to do 1-5/8 = 8/8-5/8=3/8.

Therefore, 3/8 of the bread is left.

I hope this helps!

Answer:

bcthjhrthtgtgtvrb

Step-by-step explanation:

Answer:

juhgyftchhgjhku

Step-by-step explanation:

Using Hypothesis testing, we can determine the rule for rejecting and fail to reject the null hypothesis i.e., bag is not underfilled.

It is given that distribution of data is normal in nature . It is given that bag is underfilled. We can use hypothesis testing for determine the required result. Firstly we state the Null and Alternative hypothesis,

H₀ : μ =421 : bag is not underfilled

Hₐ : μ > 421 : bag is underfilled

We have given that variance = 484 and population mean = 418

Standard deviations (σ) = √variance =√484 = 22 and n = 14

We use the Z- static test ,

Z = (X - μ) /σ/√n

Where X --> population mean

μ -->Sample mean

n --> sample size

Z = ( 418- 421) / 22 /√14 = -3 / 22 / √14

= - 0.0364, , this is one tailed test

As we know, p-value corresponding to Z-value is 0.051

The level of significance is 0.01 = 1%

i.e., α= 0.01

P-value > α

This implies null hypothesis is not rejected. So, bags are not underfilled.

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Answer/Step-by-step explanation:

43 = (4 * 101) + (3 * 100)

43 = (4 * 10) + (3 * 1)

43 = 40 + 3

Answer:

1/5

Step-by-step explanation:

In order to solve this, you need to simplify. In this case, we would need to distribute first.

-5x - (-7 - 4x) = -2(3x - 4)

-5x + 7 + 4x = -6x + 8

Combine like terms:

-5x + 7 + 4x = -6x + 8

-5x + 6x + 4x = 8 - 7

-x + 6x = 1

5x = 1

X needs to be by itself, so you would divide by 5 (the coefficient in front x) on both sides. So,

5x = 1

x = 1/5

The area bounded by the curves \(y=-6+\sqrt{x}$ and $y=\frac{-36+x}{6}$\) is 100.

The given curves are

\(y=-6+\sqrt x$ \\and $y=\frac{-36+x}{6}$\).

To find the area bounded by the curves, we need to determine the x-coordinates of their point of intersection, which is the lower and upper limits of integration.

Let's first set them equal to each other to find their point of intersection:\($$\begin{aligned}\ -6+\sqrt x&=\frac{-36+x}{6}\\ \ -36+6\sqrt x+x&=-216+36x\\ \ 5\sqrt x-35x&=-180\end{aligned}$$Now, we will set $f(x)=5\sqrt x-35x+180$ and solve for $f(x)=0$:\[f(x)=5\sqrt x-35x+180=0\]\[\begin{aligned}5\sqrt x-35x+180 &= 0\\ 5\sqrt x &= 35x - 180\\ \sqrt x &= \frac{7x-36}{5}\\ x &= \left(\frac{7x-36}{5}\right)^2\\ 25x &= (7x-36)^2\\ 25x &= 49x^2 - 504x + 1296\\ 49x^2 - 529x + 1296 &= 0\\ (7x-36)(7x-37) &= 0\end{aligned}\]\)

Thus, the x-coordinates of the intersection points are \(x=5.14$ and $x=6.17$\). The limits of integration are \(a=5.14$ and $b=6.17$\).

Therefore, the area between the curves is given by the integral:

\(\[\begin{aligned} A&=\int_a^b\left(-6+\sqrt{x}-\frac{x-36}{6}\right)dx \\ &= \int_{5.14}^{6.17}\left(-6+\sqrt{x}-\frac{x-36}{6}\right)dx\\ &=\left[-6x+\frac{2}{3}x^{\frac{3}{2}}-\frac{1}{12}x^2+\frac{36}{6}x\right]_{5.14}^{6.17}\\ &=\boxed{100}\end{aligned}\]\)

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Answer:

what is this a different answer orrrr?

The calculated chi-squared test statistic is 7.09 and the p-value is 0.0674. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the responses occur with different frequencies. So, the correct answer is A).

To find the chi-square test statistic, we need to calculate the following

Subtract the expected frequency from the observed frequency for each response and square the result. Divide each squared difference by the expected frequency. Add up all the resulting values to get the chi-square test statistic.

Using the given data table in image,

Adding up the values in the last column of data, we get

chi² = 4.05 + 1.95 + 0.92 + 0.17 = 7.09

The degrees of freedom for this test are (number of categories - 1), which in this case is 4 - 1 = 3. Using a chi-square distribution table or calculator with 3 degrees of freedom, we find the p-value to be approximately 0.0674.

Since the p-value (0.0674) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, we conclude that there is not enough evidence to suggest that the responses to the questions occur with different frequencies. So, the correct option is A).

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Answer:

58 markers

Step-by-step explanation:

52 + 6 = 58

Answer:

58 markers

Step-by-step explanation:

x-6=52 Set up the problem. "x" represents the number of markers.

 +6 +6 Add 6 to both sides to isolate x

x    =58

Answer:

x, y, and z I think that is it

Answer:

U CAN DO THIS !!!!!

Step-by-step explanation:

To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.

Herein we must prove that two circles are similar by taking advantage of two key characteristics: (i) Center, (ii) Radius. Based on such facts, we must apply the following rigid transformation:

Step 1 - Traslating the circle from A to B: Translation vector - (- 1, 1).

(x, y) = (2, 3) + (- 1, 1)

(x, y) = (1, 4)

Step 2 - Dilate the circle by a factor of 2.

r = 2 · 5

r = 10

To prove the similarity between the two circles we must translate circle A by <- 1, 1> and dilate the figure by a factor of 2.

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Given:

Markers are sold in packages of 12 and pens are sold in packages of 8.

To find:

Least amount of markers and pens Rick needs to buy to have an equal number of markers and pens

Solution:

To find the least amount of markers and pens, we need to find the LCM of 12 and 8.

Prime factors of 8 and 12 are

\(8=2\times 2\times 2\)

\(12=2\times 2\times 3\)

To find the LCM, multiply all factors but the common factors are included only once.

\(LCM(8,12)=2\times 2\times 2\times 3\)

\(LCM(8,12)=24\)

Therefore, the least amount of markers and pens Rick needs to buy to have an equal number of markers and pens is 24.

Answer:

4

Step-by-step explanation:

Coordinates of the image point A' will be (-3.6, 3.6).

  By the rule of transformation → (6a, 3a) = (7.2, 3.6)

       6a = 7.2 ⇒ a = 1.2

   Coordinates of point A → (-3, 3)

   If the point A is dilated by a scale factor 1.2 about the origin,

   Coordinates of the image point A' will be → A'(-3×1.2, 3×1.2)

                                                                          → A'(-3.6, 3.6)

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Scale factor is  \(\frac{14}{21}\).

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

Given

The rectangle on the right is a scaled copy of the rectangle on the left.

\(\frac{42}{63}\) and 15 ÷ \(\frac{45}{2}\)

\(\frac{42}{63}\)

Rationalizing \(\frac{42}{63}\) by 45

= \(\frac{42(45)}{63(45)}\)

= \(\frac{1890}{2835}\)

15 ÷ \(\frac{45}{2}\)

Rationalizing 15 ÷ \(\frac{45}{2}\) by 63

= \(\frac{30(63)}{45(63)}\)

=  \(\frac{1890}{2835}\)

If we want to find the scale factor we have to equal the proportions of two rectangles.

∴ Scale factor =  \(\frac{1890}{2835}\) = \(\frac{14}{21}\)

Hence, scale factor is  \(\frac{14}{21}\).

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Answer:  –145 is the 25th term in this series where each term is 7 less than the preceding term.

Step-by-step explanation:  Find the difference between the numbers given.

They are decreasing by 7.

The requested term is 25. Subtract -1 . = 24  (n-1)

Multiply 24 × -7 = -168

Add that to to first term

23 + (-168) = the 25th term

–145 is the 25th term in this series where each term is 7 less than the preceding term.

The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

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Answer:2

Step-by-step explanation:

If the value exceeds\($0.200$\) by the tolerance of \($0.020$\) on either side, a repair cost of \($\$150$\)is incurred.

\($L(x) = 150(x - T)$\) option b.

The Taguchi loss function measures the cost or loss associated with deviations from a target value in a quality characteristic.

In this case, the specification for the quality characteristic is \($0.200 \pm 0.020$\).

If the value exceeds \($0.200$\) by the tolerance of \($0.020$\)on either side, a repair cost of $\$150$ is incurred.

Based on this information, the Taguchi loss function for this example is given by:

b.\($L(x) = 150(x - T)$\)

In the given options, option b represents the correct Taguchi loss function. The loss function is a linear function where the loss increases linearly with the deviation from the target value.

The coefficient of \($150$\) represents the cost of repair per unit deviation.

This loss function is appropriate for the given scenario as it accurately captures the cost associated with deviations from the target value.

The Taguchi loss function provides a quantitative measure to assess the impact of variations in the quality characteristic and helps in making decisions regarding process improvement and optimization.

In this case, it allows for evaluating the cost implications of exceeding the specified tolerance and guides decision-making on whether repairs are necessary based on the associated costs.

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The following bit vector represents a disk where blocks 1,5,8,11,14 are free, and the rest is allocated is False.

What is Bit-Vector?

Bits are stored in a bit array, which is a type of array data structure. An easy set data structure can be implemented using it. Bit-level parallelism in hardware can be quickly used by a bit array to perform operations.

When files are generated, the system allots space for them by keeping track of the free disk blocks. Additionally, free space management becomes essential in order to utilise the space freed up by deleting the files.

The system keeps track of the disk blocks that are not assigned to any files or directories in a list called free space. Implementing the free space list primarily entails:

A bitmap or bit vector is a sequence or group of bits, where each bit stands for a disk block. The bit has two possible values: 0 and 1: 0 means the block is allocated, and 1 means the block is free.

A bitmap of 16 bits can be used to represent the given instance of disk blocks on the disk in Figure 1 (where green blocks are allocated) as 0000111000000110.

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Based on the hypothesis test using a significance level (α) of 0.05 and a p-value of 0.20, we fail to reject the null hypothesis, which suggests that we should not build a brick-and-mortar store.

In hypothesis testing, we compare the p-value to the significance level (α) to make a decision about the null hypothesis (H0). The null hypothesis states that there is no significant effect or relationship, while the alternative hypothesis (Ha) suggests otherwise.

In this case, the null hypothesis (H0) states that we should not build a brick-and-mortar store, and the alternative hypothesis (Ha) suggests that we should build one. When the p-value is higher than the significance level (α), it means that we do not have enough evidence to reject the null hypothesis.

Given that the p-value is 0.20 and the significance level (α) is 0.05, the p-value is greater than α. Therefore, we fail to reject the null hypothesis, indicating that there is not enough evidence to support building a brick-and-mortar store. This means that based on the statistical analysis, it would be recommended not to proceed with constructing a physical store.

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Answer:

2 or 8

Step-by-step explanation:

Place value can be defined as the numerical value representing a digit owing to its position in a number. Some examples of the various place values used in representing each digit are tenths, hundredths, thousandths, unit, tens, hundreds, thousands etc.

Given the following number;

183184

Taking the square root, we have;

√183184 = 428

Therefore, the possible "one's" digits of the square root of the number 183184 is 2 or 8.

Answer:

x= -2 y=0

Step-by-step explanation: