1 of 9
Express the ratio below in its simplest
form.
12 : 6​

Answer:

The p-value of the test is 0.0014 < 0.01, meaning that the data indicates that the true average unrestrained compressive strength is less than the design value of 3200.

Step-by-step explanation:

We want to determine whether the data indicate that the true average unrestrained compressive strength is less than the design value of 3200.

At the null hypothesis, we test if the mean is at the design value of 3200, so:

\(H_0: \mu = 3200\)

At the alternate hypothesis, we test if it is less than the design value of 3200, so:

\(H_a: \mu < 3200\)

The test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

3200 is tested at the null hypothesis:

This means that \(\mu = 3200\)

The sample average unrestrained compressive strength for 50 specimens of a particular type of brick was computed to be 3120 psi, and the sample standard deviation was 180.

This means that \(n = 50, X = 3120, s = 180\)

Test statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{3120 - 3200}{\frac{180}{\sqrt{50}}}\)

\(t = -3.14\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean below 3120, which is the p-value of t = -3.14, using a one-tailed test, with 50 - 1 = 49 degrees of freedom.

With the help of a calculator, the p-value of the test is 0.0014

The p-value of the test is 0.0014 < 0.01, meaning that the data indicates that the true average unrestrained compressive strength is less than the design value of 3200.

Answer:

Yes the rate at which death is decreasing is enclosed. Indeed I think we are safe.

Answer:

  B)  2%

Step-by-step explanation:

The simple interest formula is ...

  I = Prt

Interest I is earned on principal P when it is invested at rate r for t years.

Filling in the given values, we can solve for r:

  200 = 2000r(5)

  200/10000 = r = 2/100 = 2%

The interest rate is 2%.

Answer:

To determine the formula of g in terms of f, we would need more information about the specific transformation or relationship between f and g. Unfortunately, you mentioned that there is a graph showing f as a solid blue line and g as a dotted red line, but without additional details about the graph or the transformation, it is not possible to provide the formula of g in terms of f.

If you can provide further information about the relationship between f and g or any specific points or characteristics of the graph, I would be happy to assist you in finding the formula of g in terms of f.

Step-by-step explanation:

the answer is D

The figure can be divided into a rectangle and 2 triangles

Answer:

Step-by-step explanation:

1.) No. of student who can play an instrument= 20÷100×1,080 =0.2×1,080 = 216

2.) Minimum rate Sheila can work in =20 problems÷ 5 mins= 4 problems/min

3.) 75%

Answer:

36 cm

Step-by-step explanation:

Perimeter = sum of lenght of all sides

Perimeter = 6 + 10 + 8 + 12

Perimeter = 36 cm

To find more statements that must be true, we would need more information about the function or its derivatives.

As per the student question, we are given a twice differentiable function f(x) with some values in the table.

We know that f'(x) = 0 at x = -1, 2, and 4.

Let's analyze the given information:
1. f is a twice differentiable function, which means it has a first and second derivative, f'(x) and f''(x).
2. We are given a table of values for f(x):
  x | f(x)
 ---|-----
 -1 | -45
  0 |   0
  1 |   3
  2 |   0
  3 | -21
  4 |   0
  5 |  75
3. We know f'(x) = 0 at x = -1, 2, and 4.
Based on this information, we can deduce the following statements that must be true:
a. f(x) has at least one local minimum or local maximum at x = -1, 2, and 4 since f'(x) = 0 at these points.

These points are also known as critical points.
b. Between any two consecutive critical points, f'(x) must change its sign (from positive to negative or vice versa) as it is a twice differentiable function.

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The recursive formula for p(n) is; p(n) = p(n-2) + p(n-3) for n >= 3. Case 1: The last square is painted white. If the last square is painted white, then the second to last square must be painted gold.

There are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Case 2: The last square is painted gold. If the last square is painted gold, then the second to last square can be painted either white or gold. If the second to last square is painted white, then there are p(n-3) ways to paint the remaining n-3 squares of the checkerboard subject to the restriction.

If the second to last square is painted gold, then there are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Therefore, the recursive formula for p(n) is: p(n) = p(n-2) + p(n-3) for n >= 3

with initial conditions p(1) = 2 and p(2) = 3.

The base case for the recursion is p(1) = 2 and p(2) = 3, which are the number of ways to paint a 1 x 1 checkerboard and a 1 x 2 checkerboard subject to the restriction, respectively.

The recursive formula counts the number of ways to paint a 1 x n checkerboard subject to the restriction by considering the last column of the checkerboard.

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There are 14 dogs and 46 chickens in the farmyard.

The supposition that there are d dogs and c chickens.

Each chicken has two legs, but each dog has four.

Consequently, the total number of legs may be written as follows:

4d + 2c

Since we are aware that there are 148 legs in total, we can construct the following equation:

4d + 2c = 148

We may create another equation since we know that there are a total of 60 heads (dogs and chickens):

d + c = 60

Now that we have two equations with two variables, we may answer them both at the same time.

2d + 2c = 120 is the result of multiplying the second equation by two.

When we deduct this from the first equation, we obtain 2d = 28.

So, d = 14.

Reintroducing this into the second equation, we get:

14 + c = 60

So, c = 46.

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Answer:

A. \(\frac{1}{5} log_3(x) + log_3(y)\)

Step-by-step explanation:

Log rules tell us that multiplication inside a log can be expressed as two summands with the same base.
In other words:

\(\log_c(a*b) =\log_c(a)+\log_c(b)\)

In this case:

\(log_3(\sqrt[5]{x} * y) = log_3(\sqrt[5]{x}) + log_3(y)\)

Using log exponent rules(power can be moved to the front of a log), we get our final answer:

\(\frac{1}{5} log_3(x) + log_3(y)\)

Therefore, the values of c are 2 + 5 = 7 and 2 - 5 = -3. So, the values of c that satisfy the condition are -3 and 7.

To find the values of c such that the distance from the point (x,8) to the point (2,-4) is exactly 13 units, we can use the distance formula.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:

√((x₂ - x₁)² + (y₂ - y₁)²)

In this case, we have (x₁, y₁) = (x, 8) and (x₂, y₂) = (2, -4). Substituting these values into the distance formula, we get:

√((2 - x)² + (-4 - 8)²) = 13

Simplifying, we have:

√((2 - x)² + (-12)²) = 13

Squaring both sides of the equation to eliminate the square root, we get:

(2 - x)² + (-12)² = 13²

Expanding and simplifying:

(x - 2)² + 144 = 169

(x - 2)² = 169 - 144

(x - 2)² = 25

Taking the square root of both sides, we have:

x - 2 = ±5

Solving for x, we get:

x = 2 ± 5

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Answer:

hopefully i got this right lol

Step-by-step explanation:

First Question:

2, 1

Second Question:

I'm assuming the lawn is the shaded region, which to solve you will need to calculate the area of the trapezoid and then subtract that by the area of the building.

EQUATION for area of building: l*w

48 * 64 = 3072^2ft

EQUATION for area of trapezoid: (a+b)/2h

subsitute

(100 + 150)/2 (80) = 10000

10000 - 3072 = 6928^2 ft

Third Question:

Answer: 26 1/4

Explanation: In order to find the volume of any rectangular prism, you need to multiply the length, width, and height. In this case, the equation is: 6 * 1 1/4 * 3 1/2 = 26 1/4

THE CORRECT OPTION IS A where the input data is correct

Answer:

option 3

Step-by-step explanation:

\(AX = B\\X = A^{-1}B\\\\A = \left[\begin{array}{CC}\\2&5\\1&3\end{array}\right]\\\\\\B =\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\X =\left[\begin{array}{C}\\x&y\end{array}\right]\)

\(det A = 1\\\\adj A = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\)

\(A^{-1} = \frac{1}{det A} \times Adj A\)

      \(= 1 \times \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\\\\\\= \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\)

Therefore,

      \(X = A^{-1}B\\\\\\\left[\begin{array}{C}\\x&y\end{array}\right] = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\\)

Answer:

undefined

Step-by-step explanation:

1. Input x = -5 in function f(x):

\(5(-5) + 25 / 2(-5)^{2} - 50\)

\(-25+25 / 50 - 50\)

\(0/0\)

2. Determine the domain

\(0/0\)

undefined

\(\Large\textsf{\textbf{Answer\::}}\)

undefined

\(\Large\textsf{\textbf{Calculations\::}}\)

Plug in the value of x (-5) and simplify as follows :

\(\displaystyle\frac{5(-5)+25}{2(-5)^2-50}\)

\(\displaystyle\frac{-25+25}{2(25)-50}\)

\(\displaystyle\frac{0}{50-50}\)

\(\displaystyle\frac{0}{0}\)

We know that we can't divide by zero. Dividing by zero results in infinity , which is not a number .

So the expression is :

\(\textsf{\textbf{und.efined}}\)

\(\small\text{hope\:helpful~}\)

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Step-by-step explanation:

3x × 8x- 3x×16

24x -48x

-24x

Answer:

12/7

Step-by-step explanation:

the simplest form of 300/175 is 12/7

PLESE GIVE ME BRAINILEST

Answer:

it a 90 degree angle hope this helps:)

Step-by-step explanation:

The sum of the first 10 terms in the sequence is 195.The sequence given above is an arithmetic sequence.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each successive number is found by adding a fixed number, called the common difference, to the previous number in the sequence. The common difference is the same for each pair of consecutive numbers.

An arithmetic sequence is a sequence of numbers where each successive number is obtained by adding a fixed amount, the common difference, to the preceding number. In this particular sequence, the common difference is 5.

The first term in the sequence is a₁ = -3, and the general term is an = 3an-1 + 5, where n > 2. To find any term in the sequence, we can use the formula an = a₁ + (n - 1)d, where d is the common difference. In this case, a₁ = -3 and d = 5, so the formula becomes an = -3 + (n - 1)5.

To find the 9th term in the sequence, we can substitute n = 9 into the above formula and solve for an. This gives us an = -3 + (9 - 1)5 = -3 + 40 = 37. Therefore, the 9th term in the sequence is 37.

To find the sum of the first 10 terms in the sequence, we can use the formula Sₙ = (n/2)(2a₁ + (n - 1)d). In this case, a₁ = -3 and d = 5, so the formula becomes Sₙ = (n/2)(2(-3) + (n - 1)5). Substituting n = 10 into the formula gives us Sₙ = (10/2)(2(-3) + (10 - 1)5) = (10/2)(-6 + 45) = (10/2)(39) = 195. Therefore, the sum of the first 10 terms in the sequence is 195.

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Right Question:-

a₁ = -3,

an=3an-1+5

for

n>2.

For given sequence, Find the sum of first 10 terms?

Answer:

2 inches is longer, 7/4 inches come out to be 1.75 inches

(please mark as brainliest <3 )

Step-by-step explanation:

Answer:

2 inches is longer than \(\frac{7}{4}\) inches

Step-by-step explanation:

if we were to convert \(\frac{7}{4}\) inches to fraction form, it would be 1 \(\frac{3}{4}\), or 1.75. now, it is easier to compare. 2 is greater than 1.75

Answer:

(gof) (4) = 9

Hence, option A is true.

Step-by-step explanation:

f(x)=-x³

g(x)=|1/8x -1|

(gof) (4) = g{f(4)}

First wee need to determine f(4)

f(4)=-(4)³

    = -64

so

  (gof) (4) = g{f(4)} = g(-64)

                             =  \(\left|\frac{1}{8}\left(-64\right)-1\right|\)

                             \(=\left|-\frac{1}{8}\cdot \:64-1\right|\)

                             \(=\left|-8-1\right|\)

                             \(=\left|-9\right|\)

\(\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a\)

                             \(=9\)        

Thus,

(gof) (4) = 9

Hence, option A is true.

The expression -5(×+3)-4x+6.5  is simplified to -9x - 8.5

These are expressions composed of coefficients, terms, variables, constants and factors.

They are also made up of arithmetic operations, such as;

From the information given, we have;

-5(×+3)-4x+6.5

expand the bracket

-5x- 15 - 4x + 6.5

collect and add like terms

-9x - 8.5

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Answer:

192 markers

Step-by-step explanation:

if 8 = 4% then 2=1%

so we can assume there are 200markers in the package.

8-200= 192 markers

Answer:

11 and 31

Step-by-step explanation:

The domain of the given function is (-∞,∞),{x|x∈R} and the range of the given function is [10,90],{y|10≤y≤90}.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=40sin(0.1x+12)+50, represents the number of items, f(x), made in a factory each day for x days.

Use the derivative to find the maximum and minimum.

(5π−120,40sin(1.57079632)+50) is a local maxima

(15π−120,40sin(4.71238898)+50) is a local minima

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: [10,90],{y|10≤y≤90}

Therefore, the domain of the given function is (-∞,∞),{x|x∈R} and the range of the given function is [10,90],{y|10≤y≤90}.

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There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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