8. The speed of an object can be found by taking the distance it travels and dividing it by the
time it takes to travel that distance. An object travels 100 feet in 2.5 seconds Let the speed, be
measured in fleet per second. Write an equation to represent the relationship between the three
quantities (speed, distance, and time).

Hello!

the triangle is rectangle, so Pythagore!

c² = 15² + 8²

c² = 289

c = √289

c = 17

Answer:

RQS=110

TQS=70

Step-by-step explanation:

(12x+2)+(7x+7)=180

The two equations added together give us a straight line which is angle 180

19x + 9 = 180

19x = 171

We solve for x

x = 9

Now that we have x we plus in to each equation

RQS= (12(9)+2)

= 110

TQS=(7(9)+7)

=70

Answer:

348

Step-by-step explanation:

hope this helps

Answer:

y = 0

Step-by-step explanation:

4(y + 3) - 8 = 2(y + 2) ← distribute parenthesis

4y + 12 - 8 = 2y + 4 , that is

4y + 4 = 2y + 4 ( subtract 2y from both sides )

2y + 4 = 4 ( subtract 4 from both sides )

2y = 0 , then

y = 0

Answer:

43.98

Step-by-step explanation:

i think

The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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The value of x=32 that means after 32 weeks the number of subscribers become 64.

The term subscriber indicates how many viewers have followed to a particular channel.

In general, number of subscribers become higher day by day depending on the popularity of a channel.

given, number of subscribers become double each week

let after x week the number of subscribers will be 64

the function f(x) =2x =64

      x = 64/2 =32

hence, after 32 weeks the subscribers will be 64

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Answer:

Step-by-step explanation:

there are 1728 cubic inches in one cubic foot.

A cubic foot is 12"

12* 12" * 12" = 1728 cu/inches

therefore

1344/1728 =. 78 cu ft

Answer:

square root of 8 is 2.82842712475

If you meant 8^2 then it would be 64

Step-by-step explanation:

Answer:

The value of y from the second equation is substituted back into the first equation. What is the resulting equation?

✔ 2x + 3(8 – 3x) = 3

What is the value of x?

✔ 3

What is the value of y?

✔ –1

Using the power series expansion of cos(x) to find the sum of this series. Recall that:

cos(x) = ∑[n=0, ∞] (-1)^n (x^(2n)) / (2n)!

Comparing the given series to the power series expansion of cos(x), we have:

(-1)^n 2^(2n) / (2n)! = (-1)^n 42^n (2n)! / (2n)!

Therefore, cos(x) = ∑[n=0, ∞] (-1)^n (x^(2n)) / (2n)! = ∑[n=0, ∞] (-1)^n 2^(2n) / (2n)! = ∑[n=0, ∞] (-1)^n 42^n (2n)! / (2n)!

Setting x = 4 in the power series expansion of cos(x), we get:

cos(4) = ∑[n=0, ∞] (-1)^n (4^(2n)) / (2n)! = ∑[n=0, ∞] (-1)^n 2^(2n) / (2n)!

Therefore, the sum of the given series is cos(4) / 42 = cos(4) / 1764.

Hence, the sum of the series is cos(4) / 1764.

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-1/7, since parallel lines have equal slopes.

Answer:

18.41

Step-by-step explanation:

\(x^{2} = 12^{2} + 8^{2} - 2(12)(8)(cos 133)\\\\x= \sqrt{338.94} = 18.41\)

Answer:

Put an open circle at h= 75.5

Draw an arrow at the circle going to the right.

Answer:

40 minutes

Step-by-step explanation:

rate = distance/time = miles/hr

rate = 240 mi/2 hr = 120 mi/hr

time = distance / rate = (80 mi)/(120 mi/hr) = 0.67 hr = 40 minutes

(0.67 hr)(60 min/hr) = 40 minutes

Answer:

P = 16w - 4

Step-by-step explanation:

P = (5w-2 + 3w)2

P = (8w-2)2

P = 16w - 4

78 is the least number of tables needed to seat all the guests.

Dividing the total number of guests, 623, by the number of guests to sit per table, which is 8 guests per table, one gets 77.78 tables, rounded up to the nearest whole number, and the number is 78 tables.

The reason for rounding up is that the number of tables must be a whole number and not with a fraction or a decimal point. The first 77 tables will have all the spots fully occupied with 8 guests each, but the last table will have 7 guests with one unoccupied spot.

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Answer:

The answer is C

Step-by-step explanation:

Answer:

2 × 54,000 ÷ (1+2)

£36,000

Step-by-step explanation:

Total cost of the business = £54,000

wages : other costs = 2 : 1

Total ratio = 2 + 1 = 3

How much do I spend on wages every year?

Amount spent on wages yearly = ratio of wages / total ratio × Total cost of the business

= 2 × 54,000 ÷ (1+2)

= 2/3 × £54,000

= £108,000/3

= £36,000

Amount spent on wages yearly = £36,000

The solution of inequality is -9 < x < 12.

The correct option is B.

We have,

-2 < x/3 + 1 < 5

Now, solving the inequation in parts as

-2 < x/3 + 1

-2 - 1 < x/3

-3 < x/3

-9 < x

and, x/3 + 1 < 5

x/3 < 4

x <12

Thus, the solution of inequality is -9 < x < 12.

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The length of the ladder is approximately `17.3` feet, rounded to the nearest tenth.

Let `x` be the length of the ladder. According to the problem, the ladder is leaning against the side of a house and the angle of elevation of the ladder is `60°`. Thus, we can draw a diagram of the situation: We can now use trigonometry to find the length of the ladder. In particular, we can use the fact that the tangent of an angle is equal to the opposite side over the adjacent side.

In this case, we want to find the length of the ladder, which is the opposite side, given the angle of elevation, which is the angle opposite the ladder, and the distance from the ground to the top of the ladder, which is the adjacent side. We know that the tangent of `60°` is `√(3)`. Thus, we have:```
tan(60°) = √(3) = x/h
```where `h` is the distance from the ground to the top of the ladder. Solving for `x`, we get:```
x = h × √(3)
```We are given that the distance from the ground to the top of the ladder is `10` feet. Thus, we have:```
x = 10 × √(3) ≈ 17.3
```Therefore, the length of the ladder is approximately `17.3` feet, rounded to the nearest tenth.

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Changing any of these factors will impact the others. Increasing the sample size generally results in more accurate estimates, while increasing the desired confidence level or decreasing the acceptable sampling error requires a larger sample size.

Sample size refers to the number of individuals or observations included in a study or experiment. It is a crucial component of research design because it determines how much data can be collected and analyzed, as well as the precision and accuracy of the results.

Sampling error is the difference between the results obtained from a sample and the results that would have been obtained if the entire population had been surveyed. It is a measure of the variability between the sample estimate and the true population parameter.

In the given question,

The sample size, desired confidence level, and acceptable sampling error are all interrelated factors in statistical sampling. Changing any of these factors will have an impact on the others.

First, let's define each factor:

Now, let's discuss the effects of changing each factor:

Sample size: Increasing the sample size generally results in a more accurate estimate of the population parameter. This is because a larger sample size reduces the effect of random variability and increases the precision of the estimate.

Confidence level: Increasing the desired confidence level requires a larger sample size to achieve the same level of precision. This is because a higher level of confidence requires a wider confidence interval, which in turn requires more data points.

Sampling error: Decreasing the acceptable sampling error requires a larger sample size to achieve the same level of precision. This is because a smaller sampling error requires a narrower confidence interval, which in turn requires more data points.

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Answer: there are only 3 factors for 49 which are  1, 7, 49

The factors of 49 are as follows :

1, 7, 49  and the negative factors are : -1 , -7. -49

What mathematical factors are there?

A factor is an integer that entirely divides another number. To put it another way, if adding two whole numbers leads in a product, then the numbers we are adding are factors of the product because of product is divisible by them. There are two methods for obtaining factors: division and multiplication.

What is a Prime factor?

A natural number other than 1 in which the only factors are 1 and on its own is referred to as having a prime factor.

How is the prime  factor determined?

To use the division method to determine a number's prime factors, follow the following steps:

Step 1 : Divide the specified integer by the smallest prime number

Step 2 : Divide the quotient yet again by the smallest prime number

Step 3: Keep on in the same fashion until the quotient reaches 1.

Step 4: Multiply all the prime factors at the conclusion.

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9514 1404 393

Answer:

  +24

Step-by-step explanation:

The number of steps run can be represented by the integer +24.

The height of the triangle whose base is 4 cm and area is 20 cm² is 10 cm .

It is given that base is 4 cm and area is 20 cm² .

Putting above values in area formula , we get

         Area = 1 / 2 × base × height

            20  = 1 / 2 × 4 × height

             20 = 2 × height

              10 cm = height

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The complete question is given below :

Find the height of the triangle whose base is 4cm and area is 20 cm².

Answer:

Negative Infinity

Step-by-step explanation:

It is a negative slope, therefore as x moves towards positive infinity, y will move towards negative infinity.

Answer:

Slope: 3

Equation: y + 2 = 3(x + 1)

Step-by-step explanation:

Find the slope using (-1, -2) and (0, 1):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{0 - (-1)} = \frac{3}{1} = 3 \)

Slope (m) = 3

The equation can be represented in point-slope form, y - b = m(x - a)

Where,

(-1, -2) = (a, b)

m = 3

Plug in the values into y - b = m(x - a)

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

y + 2 = 3(x + 1)

Answer:48 oranges

Step-by-step explanation: 3 apples :4 oranges

                                             36 apples : x oranges

                                     36 times 4 which gives you 144 .Next divide 3 which give you 48.

Hope it helps  :).Please brainliest .

Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.

We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.

The null hypothesis is that the population proportion is equal to 11.3%:

H0: p = 0.113

The alternative hypothesis is that the population proportion is greater than 11.3%:

Ha: p > 0.113

The sample proportion is P = 58/400

= 0.145

The standard error of the sample proportion is:

SE = √(p*(1-p)/n)

= √(0.113*(1-0.113)/400)

= 0.0197

The test statistic is:

z = (P - p) / SE

= (0.145 - 0.113) / 0.0197

= 1.6244

The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:

p-value = P(Z > 1.6244)

= 0.0515 (using a standard normal distribution table)

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