what would the sum of x and 16 is less than 32 look like in a problem?

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Let's sum the given expressions.

We have to reduce like terms. -x and -9x are like terms. -7 and 6 are like terms.

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

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To test your hypothesis that the average time to deliver pizza, once the order is placed, is greater than 25 minutes in the population, you would perform a one-sample T-test.

1. Formulate the null hypothesis (H0) and the alternative hypothesis (H1).

In this case, H0: the average delivery time is equal to 25 minutes, and H1: the average delivery time is greater than 25 minutes.

2. Collect a sample of delivery times and calculate the sample mean and sample standard deviation.

3. Determine the appropriate T-distribution based on your sample size (degrees of freedom = sample size - 1).

4. Calculate the T-statistic using the sample mean, sample standard deviation, and sample size.

5. Determine the critical T-value based on your chosen level of significance (e.g., 0.05) and the one-tailed T-distribution.

6. Compare the calculated T-statistic to the critical T-value. If the T-statistic is greater than the critical T-value, you can reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

25 hours per week

Step-by-step explanation:

Step one:

given data

Suri makes $15 per hour and gets a weekly bonus of $25

Juan makes $14 per hour and gets a weekly bonus of $50.

Let the number of hours worked be x

and let the total earned be y

For Surl

The expression for the total is

y= 25+15x-----------1

For Juan

The expression for the total is

y= 50+14x-----------2

Step two:

Equate the two expressions we have

25+15x=50+14x

collect like terms we have

25-50= 14x-15x

-25= -x

x= 25

Yes its is possible that they earned the same amount if they work for 25 hours

Answer:

A

Step-by-step explanation:

You want the equation that best equals x^2-2x+4. What do you do? First, you want to get x^2-2x into a complete the square type of format. You'd do (x-1)^2 in the process. Next, you would add 3. Then, use POE (Process of Elimination) to consider your options. You know it can't be C or D because that would be x^2+ 2x, so in a tight race between B and A, it's A because the C term of B is 6. Hope this helps! If you need anything, let me know!!

26 square feet is the exact surface area of the composed figure with two cones.

The composed figure has two cones.

The formula to find the surface area of cone is A=πr(r+√h²+r²))

Where r is radius and h is height of the cone.

Both the cones have radius of 1 ft and height of 2ft and 4 ft.

Area of cone 1=3.14×1(1+√4+1)

=3.14(1+√5)

=10.16 square fee

Area of cone 2=3.14×1(1+√16+1)

=3.14(1+√17)

=16.01square feet.

Total surface area = 10.16+16.01

=26.17 square feet.

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We can see here that:

A cube is a three-dimensional geometric shape that has six square faces, all of which are congruent (equal in size) and perpendicular to each other. It is a special type of rectangular prism where all edges have the same length, and all angles are right angles (90 degrees).

Cubes are commonly encountered in everyday life, such as dice, boxes, and Rubik's Cube puzzles. They have precise and uniform geometry, making them useful in various mathematical and engineering applications.

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Answer:

352 lbs is correct

Step-by-step explanation:

They did estimate correctly. for how to do this look below:

So we have a elephant that gains 22 pounds every week and they estimated that at 16 week she would be at 352 lbs

22 which was current pounds at the time and she would keep gaining that every week for 16 weeks

So weight times weeks

22*16

22*16= 352

Hope this helps!

Answer:

\(x=\pm i\text{ or }x=\pm2i\)

Step-by-step explanation:

So we have the equation:

\(x^4+5x^2+4=0\)

Let's let u be equal to x². So:

\(u^2+5u+4=0\)

Factor:

\((u+1)(u+4)=0\)

Zero Product Property:

\(u+1=0\text{ or } u+4=0\)

Subtract:

\(u=-1\text{ or }u=-4\)

Replace:

\(x^2=-1\text{ or }x^2=-4\)

Take square root:

\(x=\pm\sqrt{-1}\text{ or }x=\pm\sqrt{-4\)

Simplify:

\(x=\pm i\text{ or }x=\pm2i\)

No, we cannot conclude that there is a difference in the mean number of surgeries performed by hospital or by day of the week.

The data provided would need to be further analyzed to determine if there is a statistically significant difference between the means. A t-test or ANOVA could be used to test for differences between the means.

1. The data provided shows the number of outpatient surgeries performed at three hospitals in the Tulsa, Oklahoma, area on each day of the week.

2. To determine if there is a difference in the mean number of surgeries performed by hospital or by day of the week, a statistical test needs to be conducted.

3. A t-test or ANOVA could be used to test for differences between the means.

4. The results of the test would need to be examined to determine if there is a statistically significant difference between the means.

5. At the 0.05 significance level, we cannot conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week.

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

x = 63

Step-by-step explanation:

2x - 6 = 120

2x = 126

x = 63

Answer:

x=63

Step-by-step explanation:

You put 2x-6=120. So 120+6 is 126. You then divide 126 by to and get 63.

Answer:

<3 and <4

Step-by-step explanation:

The simplified form of the polynomial expression in standard form is: - x² - 8x - 8

The standard form of a polynomial is usually expressed by writing the highest degree of terms first then the next degree and so on. The standard form of polynomial is given by, f(x) = aⁿxⁿ + aⁿ⁻¹xⁿ⁻¹ + aⁿ⁻²xⁿ⁻² + ... + a₁x + a₀, where x is the variable and a_i are coefficients.

The polynomial expression is given as (x+4)² is subtracted from 8. Thus, we have:

8 - (x+4)²

Expanding gives:

8 - (x² + 8x + 16)

= 8 - x² - 8x - 16

= - x² - 8x - 8

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Answer:

x = 23

Step-by-step explanation:

surface area of a cube = 6s²

Side length, s = x - 5

Surface area of the cube = 1944 units²

What is the value of x?

surface area of a cube = 6s²

1944 = 6(x - 5)²

1944/6 = (x - 5)²

324 = (x - 5)²

324 = x² - 10x + 25

x² - 10x + 25 - 324 = 0

x² - 10x - 299 = 0

Solve quadratic equation using factorization

(x + 13) (x - 23) = 0

x + 13 = 0 or x - 23 = 0

x = -13 or x = 23

The side length can not be negative

Therefore, x = 23

Answer:

2x = -y

Step-by-step explanation:

To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

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Answer:

2√5

Step-by-step explanation:

d = √(x2 - x1)² + (y2 - y1)²

= √[1 - (-1)]² + [3 - (-1)]

= √(2)² + (4)²

= √(4) + (16)

= √20

= 2√5

Answer:

7.5

Step-by-step explanation:

A squared + B squared = C squared

7.2 squared + 2.1 squared = C squared

=7.5

19) g(x)=0 is the value of x at points where the line cuts the x-axis

From the graph that is at:

x=-7, x=1, x=3, and x=9

20) f(x)>g(x) where the curve f(x) is higher than the curve g(x), and this is at:

x<-3, 07

Answer:

The answer is C \(\sqrt{97}\).

Step-by-step explanation:

Use the pythagorean theorem. \(a^{2} + b^{2} = c^{2}\). With a and b corresponding to the legs of the triangle.

Answer:

6 miles per hour

Answer:

Step-by-step explanation:

Rate of change = Change in Y over Change in X

Delta Y = (6-0)=6

Delta X = (2-0) = 2

Rate of change = 6/2 =3 miles per hour

Answer:

Step-by-step explanation:

Answer:

a

Step-by-step explanation: