Translate the sentence into an inequality. Eight times the sum of a number and 27 is at most "-15." Use the variable y for the unknown number.

Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.

In △ABC,

\(\longrightarrow\)sin ∠C = \(\sf \dfrac{Perpendicular}{Hypotenuse}\)

\(\longrightarrow\)sin ∠C = \(\sf \dfrac{AB}{AC}\)

\(\longrightarrow\)sin 30⁰ = \(\sf \dfrac{AB}{10\sqrt{2}}\)

\(\longrightarrow\)\(\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}\)

\(\longrightarrow\)\(\sf AB = \dfrac{10\sqrt{2}}{2}\)

\(\longrightarrow\)\(\sf AB = 5\sqrt{2}\:units\)

\(\\\)

In △ABC,

\(\longrightarrow\)cos ∠C = \(\sf \dfrac{Base}{Hypotenuse}\)

\(\longrightarrow\)cos ∠C = \(\sf \dfrac{BC}{AC}\)

\(\longrightarrow\)cos 30⁰ = \(\sf \dfrac{BC}{10\sqrt{2}}\)

\(\longrightarrow\)\(\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}\)

\(\longrightarrow\)\(\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}\)

\(\longrightarrow\)\(\sf BC = \dfrac{10\sqrt{2\times 3}}{2}\)

\(\longrightarrow\)\(\sf BC = \dfrac{10\sqrt{6}}{2}\)

\(\longrightarrow\)\(\sf BC = 5\sqrt{6}\: units\)

Thus , the length of other two sides of triangles are 5√2 and 5√6 units.

Answer:

need the answer

Step-by-step explanation:

or want me to work it out

The given statement can be formulated as follows: A batch of 150 iPads is inspected by choosing a sample of four iPads. Eight of the 150 iPads do not conform to specifications.

How many samples of four contain exactly one non-conforming iPad?

Let's solve the given problem step by step.

Step 1: We have 8 non-conforming iPads and 142 conforming iPads in the batch of 150 iPads. We need to find the number of ways to choose 4 iPads that include exactly one non-conforming iPad.

Step 2: We choose one non-conforming iPad in 8 ways and choose 3 conforming iPads in 142C3 ways, where nCk is the number of ways to choose k objects from n distinct objects without regard to order.

Thus the total number of ways to choose 4 iPads with exactly one non-conforming iPad is given by:

=8 × 142C3

\(8 \times \frac{142 \times 141 \times 140}{3 \times 2 \times 1}\)

= 2,107,280

Therefore, there are 2,107,280 samples of four that contain exactly one non-conforming iPad.

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Answer:

A. x = 24

B. x = 20

Step-by-step explanation:

→A. Add 2 to both sides:

\(\frac{x}{3} -2=6\)

\(\frac{x}{3} =8\)

→The fraction \(\frac{x}{3}\) is really just \(\frac{1}{3}x\):

→Multiply 3 to both sides:

x = 24

→B. Subtract 1 from both sides:

\(\frac{x}{5} +1=5\)

\(\frac{x}{5} =4\)

The fraction \(\frac{x}5}\) is really just \(\frac{1}{5}x\):

→Multiply 5 to both sides:

x = 20

A statistical analysis is internally valid if option B is correct, meaning that the statistical inferences about causal effects are valid for the population studied. Internal validity refers to the accuracy of conclusions drawn from a study, specifically focusing on causal relationships within the population being analyzed.

Statistical analysis is a method of examining data to identify patterns and trends, which can help researchers make informed decisions. Regression is a technique used to determine the relationship between two or more variables, where one variable (the dependent variable) is affected by one or more other variables (independent variables).

The population refers to the entire group of individuals or objects being studied. In order to have internal validity, the statistical analysis must accurately represent the population's characteristics and the causal relationships between variables.

R² (option A) is a measure of how well the regression model fits the data but doesn't necessarily imply internal validity. Option C, t-statistics, is related to hypothesis testing and helps determine if a relationship between variables is statistically significant. However, having all t-statistics greater than |1.96| doesn't guarantee internal validity.

Lastly, option D states that the population is small (less than 2,000) and can be observed. While having a smaller population might make it easier to gather data, this does not guarantee internal validity.

In summary, internal validity is achieved when the statistical inferences about causal effects are valid for the population studied (option B). It ensures that the conclusions drawn from a study are accurate and represent the true relationships within the population.

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The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 560 square feet, hence:

Area = length * width

560 = xy

y = 560/x

One side of the land is already protected by a barn, hence:

Perimeter (P) = x + x + y = 2x + y

P = 2x + y

P = 2x + 560/x

For least amount of fencing, dP/dx = 0, hence:

dP/dx = 2 - 560/x²

0 = 2 - 560/x²

560/x² = 2

2x² = 560

x = 16.7

y = 560/16.7 = 33.5 ft

The dimensions for the least amount of fencing is 16.7 ft by 33.5 ft

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If you conclude that a soda filling machine is not filling bottles completely based on the results of a sample, it means that the sample of bottles you tested showed evidence of incomplete filling.

However, it is important to note that this conclusion is based on a sample and may not represent the behavior of the entire population of filled bottles.

To make a more reliable conclusion about the filling machine's performance, you would need to conduct a statistical analysis to determine the significance of the observed incomplete filling. This analysis could involve hypothesis testing or confidence interval estimation.

Hypothesis testing allows you to assess whether the observed incomplete filling is statistically significant or could have occurred by chance. You would formulate a null hypothesis, such as "the filling machine fills bottles completely," and an alternative hypothesis, such as "the filling machine does not fill bottles completely." By comparing the sample data to the expected behavior under the null hypothesis, you can determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

The statistical analysis would involve calculating a test statistic, such as a t-test or a z-test, and determining the associated p-value. The p-value represents the probability of observing the sample data or more extreme data if the null hypothesis is true. If the p-value is below a predetermined significance level (e.g., 0.05), you would reject the null hypothesis and conclude that the filling machine is not filling bottles completely.

Additionally, you could also estimate a confidence interval for the proportion of bottles that are filled completely. This would provide a range of values within which the true proportion of completely filled bottles is likely to fall. If the lower limit of the confidence interval is below a desired threshold (e.g., 100%), it would provide further evidence that the filling machine is not consistently filling bottles completely.

It is crucial to note that drawing conclusions based on a sample has inherent limitations. The sample may not accurately represent the entire population of filled bottles, and there is always a margin of error associated with any statistical analysis. Therefore, it is recommended to conduct a larger-scale study or perform ongoing monitoring to obtain more reliable and comprehensive evidence about the filling machine's performance.

In summary, if you conclude that a soda filling machine is not filling bottles completely based on the results of a sample, it is an indication of potential issues with the machine. However, to make a more robust conclusion, you would need to conduct a statistical analysis, such as hypothesis testing or confidence interval estimation, to determine the significance of the observed incomplete filling. This analysis helps account for sampling variability and provides a more reliable assessment of the machine's performance.

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Answer:

<PTR+<RTS=180 LINEAR PAIR

<PTR=180-20=160°

Step-by-step explanation:

IN QUADRILATERAL PQRT

<P+<Q+<R+<T=360 SUM OF INTERIOR ANGLE OF QUADRILATERAL IS 360

85+<Q+70+160=360

<Q=360-315=45°

angle PQS=45°

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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Answer:

The answer is 2 hours. I put in the answer the other person said and it was incorrect. So I tried another chose and it was 2 hours.

Answer:

A) 30°

Step-by-step explanation:

All triangles angles add always to 180°, so we have two already 75° + 75° = 150° thus the angle is 30°

Answer:

m Is 30

Step-by-step explanation:

m is 30

because....the sum of angles in a triangle is 180

75+75+m =180

150+m=180

make m the subject of the formula

m=180-150

m=30

To show that w = u × v and v = w × u, we need to demonstrate that the cross product of vectors u and v yields the same result as the cross product of vectors w and u.

Given that u = v × w, let's calculate the cross product of w and u:

w × u = (u × v) × u

Since the cross product is not associative, we need to use the vector triple product identity:

w × u = u × (v × u) - (u · u) v

Since u is orthogonal to v, the dot product (u · v) is zero. Therefore, we can simplify the equation:

w × u = u × (v × u)

Next, let's calculate the cross product of v and u:

v × u = (u × v) × v

Using the vector triple product identity:

v × u = v × (u × v) + (v · v) u

Again, since u is orthogonal to v, the dot product (v · v) is zero:

v × u = v × (u × v)

Thus, we have shown that w = u × v and v = w × u, indicating that the cross products are equivalent in both directions.

In summary, when u, v, and w are orthogonal unit vectors, the cross product of u and v yields the same result as the cross product of w and u, as well as the cross product of v and w.

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The quotient of the given expression (x³+6x²+3x-10)÷(x+2) is x²+4x-5.

Given that, (x³+6x²+3x-10)÷(x+2).

Here,

x+2|x³+6x²+3x-10|x²+4x-5

 (-)x³(-)+2x²

_____________

         4x²+3x-10

   (-)4x²(-)+8x

_______________

               -5x-10

          (-)-5x(-1)-10

_______________.

                   0

Remainder = 0

Quotient = x²+4x-5

Therefore, the quotient of the given expression (x³+6x²+3x-10)÷(x+2) is x²+4x-5.

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Answer:

Just do,

Step-by-step explanation:

(X x Z) = Y

(X/Z) = Y

The solution to the system of equations graphed below is,

⇒ (0, 1)

Since, We have to given that;

Two system of equations are,

⇒ g (x) = 3x + 2

⇒ f (x) = |x - 1| + 1

Here, The graph of both system of equation are shown in graph.

We know that;

In a graph, the solution of system of equation are represented by a intersection point of both graph.

Here, In the graph of system of equation,

Intersection point is,

⇒ (0, 1)

Hence, The solution to the system of equations graphed below is,

⇒ (0, 1)

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Answer:

18

Step-by-step explanation:

Answer: I think the answer is 127 if it is wrong i am so sorry

Don't forget drop a heart.

Step-by-step explanation:

Answer:

i think 127

Step-by-step explanation:

sorry if its wrong

Answer:

x=6, x=-6

Step-by-step explanation:

Answer:

All four

Step-by-step explanation:

SSS, SAS, ASA, and HL

From the solution to the inequality, the correct interpretation is that:

Amanda's family can drive 244 miles before they need to refill the gas tank.

The amount of miles they can still travel is modeled by the following inequality:

\(108 + x \leq 352\)

It is solved similarly to an equality, hence:

\(x \leq 352 - 108\)

\(x \leq 244\)

Then:

Amanda's family can drive 244 miles before they need to refill the gas tank.

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Answer:

hope this helps!

I choose the wrong answer lol

Answer:

<2 + <3 = \(90^{o}\)

Thus, angles 2 and 3 are complementary.

Step-by-step explanation:

Complementary angles are two or more angles that their sum equals \(90^{o}\). Given that: i.  <1 and <2 are complementary

                  ii. <1 ≅ <3

                  iii. <2 ≅ <4

Prove that: <2 and <3 are complementary

Proof:

<1 + <2 = \(90^{o}\) (complementary angles)

<1 ≅ <3 (congruent property)

<2 ≅ <4 (congruent property)

⇒ <3 + <4 = \(90^{o}\) (complementary angles by congruent property)

Since <1 ≅ <3,

∴ <2 + <3 = \(90^{o}\)

Thus, angles 2 and 3 are complementary

Answer:

The answer is 100

Step-by-step explanation:

It's 100 because it's saying that the apples is 75 more grams than the pencil. So we do 25 grams plus 75 grams which gets us 100. If your wondering where I got the 25 from it's from the amount of the pencil.

The data described, the number of televisions in different households, is discrete.

discrete data consists of individual values that can be counted and are distinct from one another. In this case, the number of televisions is a discrete variable because it can only take on whole numbers, such as 0, 1, 2, 3, and so on. You cannot have a fractional or continuous number of televisions. Each household will have a specific count of televisions, and there is no intermediate value between each whole number. Additionally, the number of televisions is distinct for each household, meaning that it can differ from one household to another.

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Answer:

Step-by-step explanation:

I assume your expression is:

6x^3-60x^2+144x.

I'll use that information.

Factor 6x^3−60x^2+144x

6x^3−60x^2+144x

=6x(x−4)(x−6)

The probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.

Standard deviation = sqrt(variance) = sqrt(40,000) = 200

z = (x - μ) / σ

where z is the standardized value, x is the value of interest, μ is the mean, and σ is the standard deviation.

For x = 1000:

z1 = (1000 - 1100) / 200 = -0.5

For x = 1520:

z2 = (1520 - 1100) / 200 = 2.1

Using a calculator, we can use the normal cdf function with the z-scores to find the area between z1 and z2:

P(z1 < z < z2) = normal cdf(-0.5, 2.1) ≈ 0.9192

Rounding to four decimal places, we get:

P(1000 < x < 1520) ≈ 0.9192

Therefore, the probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.

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Thus, the ratio of Entertainment to that of Total earning by Carey is found using the bar graph as: 40:200.

A bar graph is a graphical depiction of information, amounts, or numbers employing bars or strips. They are employed to contrast and compare various data kinds, frequencies, or other measurements of several categories of data. "Bars" are the rectangles that are drawn on bar charts.

The number of articles in various categories is shown in the bars. On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.

Given data:

Carey's Monthly Budget  

Clothes   - 50

Entertainment   - 40

Bus Fare   - 30

Meals  - 60

Savings  - 20

Total earning = 50 + 40 + 30 + 60 + 20

Total earning = 200 (in dollars)

Ratio:

Entertainment / Total earning = 40/200

Thus, the ratio of Entertainment to that of Total earning by carey is found as: 40:200.

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Step-by-step explanation:

= 3/5 × 1/6

= (3 × 1)/(5 × 6)

= 3/30

= 1/10

Answer:

\( \sf \frac{1}{10} \)

Step-by-step explanation:

\( \sf = \frac{3}{5} \times \frac{1}{6} \)

\( \sf = \frac{3 \times 1}{5 \times 6} \)

\( \sf = \frac{1 \times 1}{5 \times 2} \)

\( \sf = \frac{1}{10} \)

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

d. 5(d - 4)

Step-by-step explanation:

the entrance fee is d dollars

a booklet of ride tickets cost 2.5 times the entrance fee = 2.5d

a meal ticket costs $4 less than the entrance fee = d - 4

One meal ticket costs d - 4.

Five meal tickets cost 5(d - 4).

Answer: d. 5(d - 4)