Determine whether the given equation is an absolute value function or not. 1. h(x) – 17x - 81 = -1 2.-22 + 1x - 7: = lyl B. Solve for the zeros of the following functions. Show your complete solutions. 1. h(x) = /10 – xl - 10 2. y = 7x +11+1

Answer: x =400

Step-by-step explanation:

Answer:

180 + 0.4x = 400

Answer:

Step-by-step explanation:

3x^2=6 Bring the 6 over to the left and set equation to 0

3x^2-6=0

Using the quadratic formula the answer is

x=±√2   decimal is 1.41421356 and -1.41421356

Solution of the given equation \(3x^{2}=6x\) is x=2 and 0

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given,

\(3x^{2} =6x\)

Rewrite the equation

\(3x^{2} -6x=0\)

Solve the equation

\(3x^{2} -6x=0\\3(x^{2} -2x)=0\\x^{2} -2x=0\)

Therefore the roots are

x=2 and 0

Hence, solution of the given equation \(3x^{2} =6x\) is x= 2 and 0

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Answer:

  The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

  x^5 -2 ?? x

  (-2)^5 -2 ?? (-2)

  -32 -2 ?? -2

  -34 < -2 . . . . . . not greater than

Concluding, there are (2 + 12) boxes of pencils left.

We know that Ms. Bloom had (4 + 7/12) boxes of pencils, and we also know that (2 + 1/12) of the boxes were broken.

The number of boxes of pencils left is given by the difference between the two above numbers, then we get:

N = (4 + 7/12) - (2 + 1/12) = (4 - 2) + (7/12 - 1/12) = 2 + 6/12

Now we can simplify the fraction:

N = 2 + 1/2

Concluding, there are (2 + 12) boxes of pencils left.

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The Solution:

Given:

18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7, and 31.6.

Required:

To test the claim that the mean rainfall from seeded clouds exceeds 25 ace-feet.

Step 1:

Find the mean.

Step 2:

Find the standard deviation.

Step 3:

Hypothesis:

From the Z score tables,

Since the p-value is greater than 0.05, we fail to reject the null hypothesis.

Therefore, there is no fact to support the claim that the mean rainfall exceeds 25 acre-feet.

Answer:

95

Step-by-step explanation:

I hope this help

(-19)×(-5)

Answer:

224

Step-by-step explanation:

To work out the area of any prism:

Area of cross sectional area x width

In this case, work out the area of the rectangle and multiply by 7

8 x 4 = 32

32 x 7 = 224

Answer:

10

Step-by-step explanation:

Answer:

around 81.2 degrees

Step-by-step explanation:

use inverse tangent

remeber tan = O/H

divide it first

84/13

6.461538461538462

then use invese tan(\(tanx^{-1}\))

81.20258929000894

or around 81.2 degrees

Answer:

It is 1 cent cheaper  to pay 5.46 for 7 apples.

Step-by-step explanation:

Find the unit rate:

5.46 /7 = 0.78

This is the cost for 1 apple

3.95/5 = 0.79

This is the cost for 1 apple

Answer:

5 apples for 3.95 is the better deal

Step-by-step explanation:

If you divide 7 by 5.46 you should get roughly 1.28, so $1.28 per apple

and if you divide 5 by 3.95 you should get roughly 1.26, meaning $1.26 per apple. You can verify this by multiplying 1.26 by 5 and 1.28 by 7

Answer:

  x = {-2 5/6, +2}

Step-by-step explanation:

To use the quadratic formula, it is helpful to write the equation in standard form.

  (2x +1)(3x +1) = 35

  6x^2 +5x -34 = 0 . . . . . . . subtract 35 and simplify. a=6, b=5, c=-34

The quadratic formula tells you the values of x are ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-5\pm\sqrt{5^2-4(6)(-34)}}{2(6)}\\\\=\dfrac{-5\pm\sqrt{841}}{12}=\dfrac{-5\pm29}{12}\\\\\boxed{x=\left\{-\dfrac{17}{6},2\right\}}\)

Therefore, the average value of f(x) on the closed interval [2, 6] is:-1.848

To find the average value of f(x) on the interval [2, 6], you need to use the formula for the average value of a function. That formula is given as:

average value of f(x) = (1/(b-a)) * ∫[a,b] f(x)dx

Here, a = 2 and b = 6. So, we have:

average value of f(x) = (1/(6-2)) * ∫[2,6] f(x)dx

Now, f(x) = (x² + x)cos(5x).

Therefore,∫[2,6] f(x)dx = ∫[2,6] (x² + x)cos(5x) dx

This integral can be evaluated using integration by parts.

Let u = (x² + x) and dv = cos(5x)dx.

Then, du/dx = 2x + 1 and v = (1/5)sin(5x).

Using the integration by parts formula, we have:

∫(x² + x)cos(5x)dx = uv - ∫vdu= (x² + x)(1/5)sin(5x) - ∫[(1/5)sin(5x)][(2x + 1)dx]= (x² + x)(1/5)sin(5x) - (2/25)cos(5x) - (2/25)xsin(5x) + C

Putting the limits of integration, we get:

∫[2,6] f(x)dx = [(6² + 6)(1/5)sin(5(6)) - (2/25)cos(5(6)) - (2/25)6sin(5(6))] - [(2² + 2)(1/5)sin(5(2)) - (2/25)cos(5(2)) - (2/25)2sin(5(2))]≈ -1.848

Therefore, the average value of f(x) on the closed interval [2, 6] is:-1.848

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When a postal worker counts the number of complaint letters received by the united states postal service in a given day, the type of data collected is quantitative.

Quantitative data is data that can be measured and expressed in numbers. In this case, the number of complaint letters received by the United States Postal Service in a given day can be measured and expressed as a number.

Qualitative data, on the other hand, is data that cannot be measured or expressed in numbers. For example, the contents of the complaint letters would be qualitative data.

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The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.

The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.

The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.

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Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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Answer:

A = (1/2)(7.7 + 2.3)(6) = (1/2)(10)(6) = 30 in.^2

Answer:

A = ( 7.7 + 2.3 ) x 6 / 2

A = 10 x 6 / 2

A = 60 / 2

A = 30 in^2

hope this helps:) !!!

Answer:

1/6

Step-by-step explanation:

1/3 diveded by 2/1

1/3x1/2 = 1/6

Hope it helps:)

The compound interest on N2,000 for 2 years at the rate of 10% per annum is N441.00.

Compound interest is the interest earned not only on the principal amount but also on the accumulated interest. To calculate the compound interest, we use the formula:

where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, P = N2,000, r = 0.1 (10%), n = 1 (compounded annually), and t = 2 years.

So, A = 2000\((1 + 0.1/1)^{(1*2)\) = N2,441.00

Therefore, the compound interest is N2,441.00 - N2,000.00 = N441.00.

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A 95% confidence interval is wider than a 90% confidence interval and so provides a better estimate of the population mean.

A confidence interval represents the range of values within which the population mean is estimated to lie with a certain degree of confidence. The wider the interval, the more certain we can be that the population mean lies within it. In other words, a 95% confidence interval provides a better estimate of the population mean than a 90% interval because it is wider and therefore more likely to contain the true population mean.

This increased accuracy is particularly important for the city in their budget planning as it allows them to make more informed decisions based on a more reliable estimate of their expected daily income from parking fees.

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The expression 8(5t+7v) is equivalent to the expression 2(20t+28V) and 40t + 56v option (A) and option (D) is correct.

The distributive property is the property that expresses the distributive law of algebraic multiplication. similarly, in polynomial expression we can use the distributive property for example we can write a(c+b) in the form of (ac+bc).

We have an expression:

= 8(5t+7v)

After using the distributive property, we get:

= 8×5t+8×7v

= 40t + 56v

Applying distributive property in the expression 2(20t+28v), we get:

= 2×20t+2×28v

= 40t+56v

The above expression is equivalent to the given expression.

Again applying distributive property in the expression 4(95+11v), we get:

= 4×95+4×11v

= 380+44v

The above expression is not equivalent to the given expression.

The expression 40t+7v is not equivalent to the given expression.

The expression 40t+56v is equivalent to the given expression.

Thus, the expression 8(5t+7v) is equivalent to the expression 2(20t+28V) and 40t + 56v option (A) and option (D) is correct.

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The 10th figure will have 19 blocks.

An arithmetic progression (AP) is a sequence in which the differences between each successive term are the same. The formula Tₙ = a+(n-1)d finds the general term (or) nth term of an AP whose first term is 'a' and the common difference is 'd'.

In the given figures,

Figure 1 has 1 block.

Figure 2 has 3 blocks.

Figure 3 has 5 blocks.

We have to find the number of blocks in the 10th figure.

The number of blocks in the figures are forming an arithmetic progression of 1,3,5.....with a common difference of 2.

So the 10th term of AP can be calculated as,

\(T_{10} = 1 + (10 -1)2\)

\(T_{10} = 1 + 9*2\)

\(T_{10} = 19\)

Therefore, the 10th figure will have 19 blocks.

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The equation of G which is a transformation of y = sin x is

The coordinates of point P is (3π/2, 1)

Equation of graph G is as a result of transformation of graph of y = sin  x. The transformation type is translation and the rule is: up, 4 units. This is written as:

y = sin  x

G(x) = y + 4 = sin  x + 4

G(x) = sin  x + 4

The plot of the graph of G(x) = sin  x + 4 shows that the coordinate of point P is

(3π/2, 1)

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Answer:

Step-by-step explanation:

With range, you subtract the greatest unit, by the smallest.

8- (-4) = 4

So the answer would be 4.

Answer: 12

Step-by-step explanation: To find the range, we first need to order the numbers from least to greatest:

-4, -2, -1, 0, 1, 8

Now, we subtract the greatest number from the smallest number. In this case, it'd be 8 - (-4)

So, that'd be 12. I hope this helped!

Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.

When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:

Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.

Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.

Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.

Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.

Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.

Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.

These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.

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The probability of getting a poker hand (5 cards) containing 3 cards of one denomination and 2 cards of a second denomination or full house is 0.00144 or about 0.14%.

To calculate the probability of getting a full house, we need to first determine the total number of possible 5-card hands. This can be done using the formula for combinations:

C(52, 5) = 2,598,960

There are 2,598,960 possible 5-card hands from a standard deck of 52 cards.

Next, we need to count the number of ways to get a full house. To do this, we first choose the denomination for the 3-of-a-kind (there are 13 options), then choose which 3 of the 4 cards of that denomination to include (there are C(4,3) ways to do this), and finally choose the denomination for the pair (there are 12 remaining denominations to choose from), and which 2 of the 4 cards of that denomination to include (there are C(4,2) ways to do this). So the total number of full houses is:

13 * C(4,3) * 12 * C(4,2) = 3,744

Therefore, the probability of getting a full house is:

P(full house) = 3,744 / 2,598,960

≈ 0.00144

So the probability of getting a full house is approximately 0.00144 or about 0.14%.

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Answer:

\(30x+85y\leq 250\)

Step-by-step explanation:

Cost of each part is \(\$85\)

Cost of working one hour is \(\$30\)

Let number of hours worked be \(x\) and

number of parts bought be \(y\).

The maximum amount of money that John can spend is \(\$250\).

From the question we have

\(30x+85y\leq 250\)

The required inequality is \(30x+85y\leq 250\).

Answer:

1st option

y=-3/8x+3

Answer:

3.5 is your answer.

Step-by-step explanation:

2.6  

0.9+

------

3.5

Answer

3.5

Explanation

2.6 + 0.9

3.5

Good Luck ^-^