Solve the inequality

-7x + 12 = 75

The graph is a downward-opening parabola opening downward with its vertex at (2,0). Therefore, the correct option is C.

The equation y = -16t^2 + 64t + 16 represents the path of a projectile launched from a 16-ft-tall tower. To determine the correct graph, we can analyze the equation. The coefficient of t^2 (-16) is negative, indicating a downward-opening parabola. The coefficient of t (64) determines the horizontal shift of the graph, and in this case, t = 4 represents the maximum height of the projectile. The constant term (16) represents the initial height of the tower.

Considering these factors, we find that the correct graph of the equation is option C. It depicts a downward-opening parabola with its vertex at (2,0). The parabola starts at an initial height of 16 ft (the tower's height) and descends symmetrically from its vertex.

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Answer:

Step-by-step explanation:

you got this i believe in you!

The calculated value of x in the right angled triangle is 28.3 units

Given that we have a right angled triangle

In a right triangle, the cosine of an acute angle is defined as the ratio of the length of the adjacent side ot the hypotenuse

The cosine function is abbreviated as "cos" and is represented as:

cos(theta) = adjacent/hypotenuse

So, we have

cos(50) = x/44

This gives

x = 44 * cos(50)

Evaluate

x = 28.3

Hence, the value of  x is 28.3

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Answer:

The volume of the shark tank is \(2160 m^3\)

Step-by-step explanation:

The tank is in the shape of a rectangular prism.

The length of the tank, \(l=18\) m.

The width of the tank, \(w=15\) m.

The height of the tank, \(h=8\) m.

We know that, volume of a rectangular prism \(=l\times w \times h\).

So, the volume of the tank \(=18\times 15\times 8=2160 m^3\)

Hence, the volume of the shark tank is  \(2160 m^3\).

Answer:

The slope is -3/5=-0.6

Step-by-step explanation:

Slope: (5-8)/(8-3)= -3/5=-0.6

Answer:

\(m=-\frac{3}{5}\)

Step-by-step explanation:

Step 1: Slope

Step 2: Set up equation and solve for m

Answer:

Step-by-step explanation:

The perimeter is all the side lengths added together

In this case, the

perimeter = x + (x+4) + (x+6) = 3x + 10

The correct answer is the first choice

Answer:

x=-15/2 and x=1

x=6 and x=3/4

Step-by-step explanation:

You have the following equations:

\(\frac{4x-3}{x+2}=\frac{2x}{x+5}\)

\(\frac{2}{x-2}+\frac{3}{x}-\frac{9}{x+3}\)

To solve both equations you can first multiply by the m.c.m of the denominators, and then solve for x, just as follow:

first equation:

\([\frac{4x-3}{x+2}=\frac{2x}{x+5}](x+2)(x+5)\\\\(4x-3)(x+5)=2x(x+2)\\\\4x(x)+4x(5)-3(x)-3(5)=2x(x)+2x(2)\\\\4x^2+20x-3x-15=2x^2+4x\\\\4x^2-2x^2+20x-3x-4x-15=0\\\\2x^2+13x-15=0\)

In this case you use the quadratic formula:

\(x_{1,2}=\frac{-13\pm \sqrt{(13)^2-4(2)(-15)}}{2(2)}\\\\x_{1,2}=\frac{-13 \pm 17}{4}\\\\x_1=-\frac{15}{2}\\\\x_2=1\)

Then, for the first equation the solutions are x=-15/2 and x=1

second equation:

\([\frac{2}{x-2}+\frac{3}{x}=\frac{9}{x+3}]x(x-2)(x+3)\\\\2x(x+3)+3(x-2)(x+3)=9x(x-2)\\\\2x^2+6x+3(x^2+3x-2x-6)=9x^2-18x\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\2x^2+6x+3x^2+3x-18-9x^2+18x=0\\\\-4x^2+27x-18=0\)

Again, you use the quadratic formula:

\(x_{1,2}=\frac{-27\pm \sqrt{(27)^2-4(-4)(-18)}}{2(-4)}\\\\x_{1,2}=\frac{-27\pm 21}{-8}\\\\x_1=6\\\\x_2=\frac{3}{4}\)

Then, the solutions for the second equation are x=6 and x=3/4

What's the question:

whats the question

What's the question:

whats the question

Answer:

Try typing into a scientofic calculator I reccomed the site desmos

Step-by-step explanation:

Answer:

12a + 8b

Step-by-step explanation:

There isn't An outcome due to the fact that it needs more to be worked out, but that's the simplified form, I believe that's what they wanted to know.

Hope It Helps!

Yes.

The data are from a random sample, meeting the Randomization Condition.

The data have at least 10 successes and 10 failures, meeting the Success/Failure Condition.

The population is much larger than the sample, meeting the 10% Condition. A

It is reasonable for the research team to use a Normal model for the sampling distribution of the sample proportion.

A Normal model for the sampling distribution of a sample proportion, three conditions must be met:

The Randomization Condition, the Success/Failure Condition, and the 10% Condition.

The Randomization Condition is met as the sample is selected randomly from a much larger population of adults.

The Success/Failure Condition is also met because the sample size is large enough (n = 1900) for us to expect at least 10 successes (those who are pessimistic about the future of marriage and family) and 10 failures (those who are optimistic about the future of marriage and family).

The sample proportion of pessimistic adults is 34%, which corresponds to 646 successes in the sample.

The 10% Condition is also met as the sample size (n = 1900) is less than 10% of the total population of adults.

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Answer:

4x - 43

Step-by-step explanation:

7x - 28 - 3x - 15

7x - 3x - 28 - 15

4x - 43

The simplified expression is 4x - 43.

The correct option is A.

A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.

As per the information provided, it is given that,

7(x - 4) - 3(x + 5)

Expanding the brackets and simplifying, we get:

7(x - 4) - 3(x + 5)  = 7x - 28 - 3x - 15

7(x - 4) - 3(x + 5)  = 4x - 43

Therefore, the expression is 4x - 43.

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Answer:

y=125a+1

Step-by-step explanation:

Answer:

it is 15 percent decay

Step-by-step explanation:

The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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To evaluate the function at each specified value of the independent variable,(a) f(-2) = 13, (b) f(1/2) = 9, (c) f(1) = 9

To evaluate the function at each specified value of the independent variable, we substitute the given values into the corresponding piecewise-defined function.

(a) For f(-2), since -2 is less than 0, we use the first piecewise function:  f(x) = 9 - 2x. Plugging in x = -2, we have f(-2) = 9 - 2(-2) = 9 + 4 = 13.

(b) For f(1/2), since 1/2 is greater than 0 but less than 1, we use the second piecewise function: f(x) = 9. Plugging in x = 1/2, we have f(1/2) = 9.

(c) For f(1), since 1 is equal to 1, we use the third piecewise function: f(x) = 8x + 1. Plugging in x = 1, we have f(1) = 8(1) + 1 = 8 + 1 = 9.

Therefore, the function evaluated at each specified value is:

(a) f(-2) = 13

(b) f(1/2) = 9

(c) f(1) = 9.

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We are given a trapezoid and we are asked to determine one of its angles. To do that we need to have into account that the following angles are equal:

Also, the sum of two different angles must be equal to 180, therefore, we have the following relationship:

Replacing the value of angle W:

Subtracting 112 to both sides:

Therefore, the measure of angle Z is 68.

Billy's total annual health insurance premium is $4,712.54. Then the correct option is D.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Billy’s employer pays for 65% of his annual health insurance premium.

Billy has the rest deducted in equal amounts from his paycheck.

If billy has $105.73 withheld from his paychecks twice each month.

His employer contributes towards his health insurance on an annual basis.

To get the amount of his employer to contribute towards his health insurance on an annual basis will be

105.73 × 24 = 2537.52

The next step is to calculate Billy's total annual health insurance premium will be

\(\rm Health \ insurance \ premium = \dfrac{2537.52 * 0.65}{0.35}\\\\Health \ insurance \ premium = 4712.54\)

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Answer: 25 books.

Step-by-step explanation:

Let as consider we need to find "how many books did Mr. Wharton buy in all?​"

Let total number of books bought by Mr. Wharton be x.

80% of all the books she bought were paperbacks.

\(Paperbacks=x\times \dfrac{80}{100}=0.8x\)

It is given that the number of paperbacks is 20.

\(0.8x=20\)

Divide both sides by 0.8.

\(x=\dfrac{20}{0.8}\)

\(x=25\)

Therefore, Ms Wharton bought 25 books in all.

Answer:

For Apex: C, 25

Step-by-step explanation:

When a value is randomly selected from a normal distribution, find the probability that it will be counted as an outlier. Rounded to three decimal places, the answer is 0.007.

Consider the standard normal distribution. To find P(Z > right fence or Z < left fence), we must first find the value of the right and left fences. Outliers are defined as data values that are above the right fence q3 1.5(iqr) or below the left fence q1 - 1.5(iqr), where iqr is the interquartile range. The interquartile range can be calculated using the following formula:IQR = Q3 – Q1where Q3 and Q1 are the 75th and 25th percentiles, respectively.To calculate the right fence, we use the formula:

Right fence = Q3 + 1.5(IQR).

To calculate the left fence, we use the formula:

Left fence = Q1 - 1.5(IQR).

Since the problem only provides information about the standard normal distribution, we will use Z-scores to find the probability that a value is an outlier. We use the Z-score formula:

Z = (x - μ) / σ where x is the observed value, μ is the mean, and σ is the standard deviation. Because we are using the standard normal distribution, the mean is zero and the standard deviation is one.We now have all of the information we need to calculate the probability of an outlier.

P(Z > right fence or Z < left fence) = P(Z > right fence) + P(Z < left fence).We first calculate P(Z > right fence):P(Z > right fence) = P(Z > (Q3 + 1.5(IQR) - μ) / σ) = P(Z > (Q3 + 1.5(IQR)))

Using the standard normal distribution table, we look up the value of Z for (Q3 + 1.5(IQR)) to get: P(Z > right fence) = P(Z > 2.698) = 0.0034. Next, we calculate P(Z < left fence): P(Z < left fence) = P(Z < (Q1 - 1.5(IQR) - μ) / σ) = P(Z < (Q1 - 1.5(IQR))). Using the standard normal distribution table, we look up the value of Z for (Q1 - 1.5(IQR)) to get:P(Z < left fence) = P(Z < -2.698) = 0.0034. Therefore, P(Z > right fence or Z < left fence) = 0.0034 + 0.0034 = 0.0068, which, rounded to three decimal places, is 0.007.

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To find the probability that a value randomly selected from a normal distribution will be counted as an outlier, we need to convert the values of the fences into z-scores using the standard normal distribution.

The formula for finding the z-score of a value x is:

z = (x - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution.

For the right fence, we have:

right fence = Q3 + 1.5(IQR)

We can convert Q3 and IQR into z-scores using the formula above, since they are also measures of central tendency and dispersion.

z(Q3) = (Q3 - μ) / σ

z(IQR) = IQR / σ

Using the properties of quartiles and the fact that the normal distribution is symmetric, we know that Q3 is located at approximately z = 0.67.

To find IQR, we need to calculate the difference between the 75th and 25th percentiles:

IQR = Q3 - Q1

Since the normal distribution is symmetric, we can assume that Q1 is located at approximately z = -0.67.

Therefore:

z(Q3) = (0.67 - 0) / 1 = 0.67

z(IQR) = (0.67 - (-0.67)) / 1 = 1.34

z(right fence) = z(Q3) + 1.5 * z(IQR) = 0.67 + 1.5 * 1.34 = 2.67

Similarly, we can calculate the z-score for the left fence:

left fence = Q1 - 1.5(IQR)

z(left fence) = z(Q1) - 1.5 * z(IQR) = -0.67 - 1.5 * 1.34 = -3.00

Now that we have the z-scores for the fences, we can use the standard normal distribution table or calculator to find the probabilities:

P(Z > 2.67) = 0.003

P(Z < -3.00) = 0.001

The probability of randomly selecting a value that is an outlier is therefore:

P(Z > 2.67 or Z < -3.00) = P(Z > 2.67) + P(Z < -3.00) = 0.003 + 0.001 = 0.004

Therefore, the probability of randomly selecting a value from a normal distribution that will be counted as an outlier is 0.004, rounded to 3 decimal places.

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The value of the variables m and n are 3/2 and 4 respectively

Noe that quadratic functions are defined as functions having its degree as 2.

The general formula for a quadratic function is expressed as;

ax² + bx + c

Standard form

ax² + bx + c = 0

Given the illustration, we have that the two functions have similar roots.

Then, we have;

The value of n = 4

For the value of m, we represent it thus; (-b/a)

-5x/m = -10x/3

cross multiply the values, we get;

m = 3(-5x)/-10x

m = 3/2

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Answer:

414.72

Step-by-step explanation:

Answer:

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Step-by-step explanation:

414.72

Example of an undecidable problem is given by the problems in the system created by computer viruses.

According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.

A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.

whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.

If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.

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The expression is always true, regardless of whether the individual propositions are true or false. This is because the logical structure of the expression ensures that if any of the individual propositions are true, then the entire expression must be true. Therefore, we can conclude that ( ∨)∧(→)∧( →)→∨ is a tautology.

To determine whether ( ∨)∧(→)∧( →)→∨ is a tautology or a contradiction, we can use truth tables. A truth table is a way of showing all the possible combinations of truth values for the variables in an expression and evaluating the expression for each combination.

In this case, we have four variables. Each of these variables can have a truth value of either true or false. We can construct a truth table for this expression as follows:

| | | | | | | | | |
|-|-|-|-|-|-|-|-|-|
| | | | | | | | | |
|T|T|T|T|T|T|T|T|T|
|T|T|T|T|F|F|F|F|T|
|T|T|F|F|T|T|F|F|T|
|T|F|T|F|T|F|T|F|T|
|T|F|F|T|T|F|F|T|T|
|F|T|T|F|F|T|T|F|T|
|F|T|F|T|F|T|F|T|T|
|F|F|T|T|T|T|F|F|T|
|F|F|F|F|T|T|T|T|T|

The last column of the truth table shows the result of evaluating the expression for each combination of truth values. We can see that the expression is always true, regardless of the truth values of the variables. Therefore, ( ∨)∧(→)∧( →)→∨ is a tautology.

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Answer:

ZB= 39°

Step-by-step explanation:

complementary angles are angles that add up to equal 90

equation:  7x + 23 + 5x + 19 = 90

add like terms: 12x + 42 = 90

subtract 42 from both sides: 12x = 48

divide both sides by 12: x = 4

plug in the value of x to the equation for ZB: 5(4) + 19

simplify: ZB= 39°

The exact length of the shadow cast by the lamp post is 15√3 feet.

We can use the tangent function to solve this problem.

Let's call the length of the shadow x.

We have the angle of elevation of the sun as 60º and the height of the lamp post as 15 ft.

From trigonometry, we know that:

tan 60º = opposite / adjacent

In this case, the opposite side is the length of the shadow (x), and the adjacent side is the height of the lamp post (15 ft).

So we can write:

tan 60º = x / 15

We can simplify the equation using the value of tangent for 60º, which is √3. So we have:

√3 = x / 15

Multiplying both sides by 15, we get:

x = 15 ×√3

Therefore, the exact length of the shadow cast by the lamp post is 15√3 feet.

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The intersection of line m and line n can have different characteristics based on the given information. However, since no specific details are provided about the relationship between line m and line n, we cannot determine their intersection type with certainty.

Here are some possible scenarios:

1. Concurrent Lines: If line m and line n lie in the same plane and intersect at a single point W, they are called concurrent lines. The intersection point W is unique and lies on both lines.

2. Parallel Lines: If line m and line n lie in parallel planes and do not intersect, they are called parallel lines. In this case, there is no intersection point between the two lines.

3. Skew Lines: If line m and line n do not lie in the same plane and are not parallel, they are called skew lines. Skew lines do not intersect, and there is no common point between them.

Without additional information specifying the relationship between line m and line n, it is not possible to determine the exact type of intersection. To provide a more accurate answer, it would be helpful to know if any additional planes or lines are involved or if there are any specific conditions or constraints given in the problem statement.

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The smallest p-value is always associated with the z-score that is furthest away from the mean. This is because the tails of the normal distribution curve have less area and thus represent smaller p-values. The correct answer is option (d) z = -3.24.

In a hypothesis test, there are two hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1).

The null hypothesis is the one we're testing, while the alternative hypothesis is the one we're trying to support or prove.

A two-tailed alternative hypothesis is one in which we are interested in whether a parameter is not equal to a certain value, as opposed to one-tailed alternative hypotheses, in which we are interested in whether the parameter is greater than or less than a certain value.

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