Solve for x. Show your work.
5(x + 2) = 3x - 16

Answers:

=============================================================

Explanation:

The smaller angles QRT and TRS combine to the angle QRS which is 90 degrees.

(angle QRT) + (angle TRS) = angle QRS

(2x) + (8x) = 90

10x = 90

x = 90/10

x = 9

We'll then use this x value to find each angle

As a way to check the answer,

angle QRT + angle TRS = 18+72 = 90

so the answer is confirmed.

1) To determine if the triangle is acute, obtuse, or right, we need to check if the sum of the squares of the two shorter sides is greater than, equal to, or less than the square of the longest side.

Let's first arrange the side lengths in ascending order:

28 in. < 34 in. < 42 in.

Now we can apply the Pythagorean theorem:

28² + 34² = 196 + 1156 = 1352

42² = 1764

Since 1352 is less than 1764, the sum of the squares of the two shorter sides is less than the square of the longest side. Therefore, the triangle is obtuse.


2)

We can use the tangent function to find the length of BC.

tan(B) = opposite/adjacent

We know that the opposite side of angle B is BC, and the adjacent side is AC, which is the height of the triangle. Since angle B is 45 degrees, we have:

tan(45) = BC/16

Simplifying the left side using the fact that tan(45) = 1, we get:

1 = BC/16

Multiplying both sides by 16, we get:

BC = 16

Therefore, the length of BC is 16 ft.


3)

Since the hypotenuse of each triangular quilt piece is 18 inches, we can use the Pythagorean theorem to find the length of each side. Let's call one leg of the triangle x (since the two legs will be equal), and the hypotenuse is 18. Then:

x² + x² = 18²

Simplifying:

2x² = 324

Dividing by 2:

x² = 162

Taking the square root:

x = √(162) = sqrt(2 * 3⁴)

We can simplify this by breaking it down into factors:

x = 3 * √(2) * 3

x = 9√(2)

Therefore, the length of each side of the triangular quilt piece is 9√(2) inches or 12.73 inches


4)

We can use the inverse sine function to find the angle that has a sine of 9/16. Using a calculator, we get:

sin^(-1)(9/16) ≈ 35.54°

Therefore, the missing value is approximately 35.54°

5)
We can use the inverse cosine function to find the angle that has a cosine of 7/18. Using a calculator, we get:

cos^(-1)(7/18) ≈ 61.48°

Therefore, the missing value is approximately 61.48°


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The correct property of the quadratic parent function is given by:

B. Its vertex is at the origin.

The quadratic parent function is modeled by:

y = x².

It has the vertex at the origin and increases to the left and to the right, into quadrants I and II, forming a function that is graphed by a parabola.

Hence the correct option regarding a property of the quadratic parent function is given by:

B. Its vertex is at the origin.

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Answer:

the subtraction property of equality

Step-by-step explanation:

trust

Answer:

Subtraction

Step-by-step explanation:

Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57

Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.

Thus, the cows whose feed includes seaweed is 74/124

= 0.59677419354

≈ 0.597

The Probability of those whose feed is without sea weed is

Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.

Thus, the probability is 40/70
= 0.5714285714

≈ 0.571

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To find the missing value of x in a triangle, subtract the sum of the two angles from 180 degrees.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Having three edges and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C.

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

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a) Rocky Mountain should order 200 tires each time it places an order.

b) The total cost of this policy is $17,160.

a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:

If fewer than 200 tires are ordered: The purchase price is $25 per tire.

If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.

If 8,000 or more tires are ordered: The purchase price is $13 per tire.

Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.

b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:

Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200

Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950

Therefore, the total cost of this policy is $40,950.

Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.

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The dissociation curve is a graphical representation of the relationship between the fractional saturation of hemoglobin (Y-axis) and the partial pressure of oxygen (X-axis) under specific conditions. It provides important information about the binding and release of oxygen by hemoglobin.

The dissociation curve for hemoglobin exhibits a sigmoidal (S-shaped) shape. At low partial pressures of oxygen, such as in tissues, hemoglobin has a low affinity for oxygen and only binds a small amount. As the partial pressure of oxygen increases, hemoglobin's affinity for oxygen increases, resulting in a rapid increase in the binding of oxygen molecules. However, once the hemoglobin becomes nearly saturated with oxygen, the curve levels off, indicating that further increases in partial pressure have minimal effects on oxygen binding.

To calculate the fractional saturation of hemoglobin at a given partial pressure of oxygen, you can use the Hill equation:

Y = [O2]^n / ([O2]^n + P50^n)

Where:

Y is the fractional saturation of hemoglobin,

[O2] is the partial pressure of oxygen,

P50 is the partial pressure of oxygen at which hemoglobin is 50% saturated,

n is the Hill coefficient, which represents the cooperativity of oxygen binding.

To determine the P50 value experimentally, the partial pressure of oxygen at which hemoglobin is 50% saturated, you can plot the dissociation curve and identify the point where the curve reaches 50% saturation.

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The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.

This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.

According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.

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The length of major arc ACD in the circle with center D is given as (325/36)π feet

An equation is an expression that shows the relationship between two or more numbers and variables.

The length of major arc ACD = [(360 - 35) / 360) * 2π(10/2) = (325/36)π feet

The length of major arc ACD in the circle with center D is given as (325/36)π feet

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It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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Answer:

$6750.50

Step-by-step explanation:

F = Pe^(rt)

8327.94 = P × e^(0.0175 × 12)

P = 8327.94/e^0.21

P = 8327.94/1.23376806

P = 6750.5

Based on the calculations we have rejected the null hypothesis .

Given,

Standard deviation = $ 45

Random sample = 20

Now,

Part 1

Set the null hypothesis and alternative hypothesis,

\(H_{0} : u = 0\\ H_{0} : u > 606.40\)

Part 2

The value of z critical signifies 5% level of significance .

\(Z_{0.05} = 1.65\)

According to critical value if z after calculation is greater than or equal to 1.65 we reject the null hypothesis .

Part 3

The value of Z can be calculated by the formula,

Z = X - µ/σ/√n

Substitute the values ,

Z = 628.85 - 606.40/45/√20

Z = 1.93

Part 4

From the above calculation the value of Z is greater than the critical value .

Thus we reject the null hypothesis .

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Answer:

Decrease by 5.5 percent

1-.945 = .055

= 5.5 percent

Answer:

The answer is a rotation 90

Step-by-step explanation:

Start with your exponetial growth formula: y = a(1 + r)^t.

Now, a is going to be your initial amount, r is the rate, and t is the time.

So we have y = $4,000(1 + .02)^7.

Now simplify inside the parenthses first.

So we have y = $4,000(1.02)^7.

Simplifying further gives us y = $4,000(1.14868).

Now use a calculator to get y = $4,594.72

There were 7 number of pieces that were in the puzzle that took the child 30 seconds to complete,that can be found using the data given & the coordinates on the graph (7,30) which indicates the number of pieces as 7 and time as 30 sec.

What is data?

Data is the collected information that can be arranged and used for analysing or interpretation. The collected data is also called as raw data, which further needs to be arranged. The data can be represented visually, in tabular form , grouped or ungrouped form. Pictographs, bargraphs, box-whisker plot, line plot, histogram, pie chart are the visual representations.

Here given that the data is arranged in the form of graph containing x-axis & y-axis. Data collected/arranged represents the number of pieces contained in the puzzle & the time taken to solve it.

X-axis represents the number of pieces in the puzzle & Y-axis represents the time taken to complete that.

The points plotted on graph are:

(4,15): Number of pieces=4

         Time taken to complete=15 seconds

(5,15):Number of pieces=5

         Time taken to complete=15 seconds

(7,30): Number of pieces=7

         Time taken to complete=30 seconds

(8,25): Number of pieces=8

         Time taken to complete=25 seconds

(12,40): Number of pieces=12

         Time taken to complete=40 seconds

∴The puzzle that was completed by child in 30 seconds contained 7 pieces.

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Refer to the attachment for the graph.

Answer:

x^2 + 6x + 8

Step-by-step explanation:

area of blue = x^2

area of pink= 2x

area of green=4x

area of brown=8

Adding all the area.

we get : x^2 + 6x +8

Answer:

205 is my answerrrrrrrrrrr

The best prediction of the time required for the oil spill to reach a diameter of 10 km will be 147 days. Then the correct option is A.

The quadratic equation is given as ax² + bx + c = y. Then the degree of the equation will be 2.

The table shows the connection between the width in kilometers of an oil slick and the time in days. A capability can be utilized to show this relationship.

The equation at (2.4, 1) will be given as,

2.4 = a (1)² + b (1) + c

2.4 = a + b + c                 ...1

The equation at (9.4, 2) will be given as,

9.4= a (2)² + b (2) + c

9.4 = 4a + 2b + c                 ...2

The equation at (21.1, 3) will be given as,

21.1 = a (3)² + b (3) + c

21.1 = 9a + 3b + c                 ...

Solve equations 1, 2, and 3 with the calculator, then we have

a = 2.35, b = -0.05, c = 0.1

Then the equation is given as,

y = 2.35x² - 0.05x + 0.1

The best prediction of the time required for the oil spill to reach a diameter of 10 km will be

y = 2.35(10)² - 0.05(10) + 0.1

y = 235 - 0.5 + 0.1

y = 235.5

The value of y is nearer to the value of 233. Then the value of y will be 233 days.

The best prediction of the time required for the oil spill to reach a diameter of 10 km will be 233 days. Then the correct option is D.

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Answer:

y = 108 degrees

Step-by-step explanation:

Set 2x + 16 and 3x - 12 equal to each other.  Subtract 2x on both sides to get this equation 16 = x - 12, add 12 on both sides to get 28 as your x value.  Plug in x for 3x - 12.  You should get 72 degrees on one side and 108 degrees on another side as y since FE makes up as a straight angle.

Answer:

sin -115 = -0.91, cos -115 = -0.42

Step-by-step explanation:

The sine and cosine of -115 degrees sin -115 = 0.91 and   cos -115 degrees = -0.42.

Since sine and cosine are both periodic functions, their values repeat every 360 degrees. Therefore, the sine and cosine of -115 degrees are the same as the sine and cosine of 115 degrees, respectively.

So, sin -115 = 0.91 and cos -115 degrees = -0.42.

Here is a table of the sine and cosine of angles from 0 to 360 degrees:

Angle | Sine | Cosine

------- | -------- | --------

0 degrees | 0 | 1

30 degrees | 0.5 | 0.866

45 degrees | 0.707 | 0.707

60 degrees | 0.866 | 0.5

90 degrees | 1 | 0

120 degrees | 0.866 | -0.5

135 degrees | 0.707 | -0.707

150 degrees | 0.5 | -0.866

180 degrees | 0 | -1

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Answer:

?

Step-by-step explanation:

Answer:

45 & 47

Step-by-step explanation:

Forming the equation,

→ x + (x + 2) = 92

→ 2x + 2 = 92

Now the value of x will be,

→ 2x + 2 = 92

→ 2x = 92 - 2

→ x = 90/2

→ [ x = 45 ]

Then the required integers are,

→ x = 45

→ x + 2 = 45 + 2 = 47

Hence, the integers are 45, 47.

Answer:

(a) 1.353 x 10^9

Step-by-step explanation:

Jumping 9 places back to obtain standard form

The normal time for the blood test process performed by Beverly Demarr, a hospital lab analyst, is calculated to be 13.92 minutes. The standard time for the blood test is determined to be 14.04 minutes.

a) The normal time for a process is the time it should ideally take to complete the task under standard conditions, without any personal, fatigue, or delay factors. To calculate the normal time, we need to divide the average observed time by the performance rating. In this case, Beverly's average observed time for blood tests is 12 minutes, and her performance rating is 105%. Therefore, the normal time for the process is calculated as follows:

Normal Time = Average Observed Time / Performance Rating

Normal Time = 12 minutes / 105%

Normal Time ≈ 11.43 minutes

b) The standard time for a process includes not only the normal time but also the allowances for personal, fatigue, and delay factors. The total allowance is 16% of the normal time. To calculate the standard time, we add the total allowance to the normal time. Using the calculated normal time of 11.43 minutes, we can determine the standard time as follows:

Total Allowance = Normal Time× Allowance Percentage

Total Allowance = 11.43 minutes × 16%

Total Allowance ≈ 1.83 minutes

Standard Time = Normal Time + Total Allowance

Standard Time = 11.43 minutes + 1.83 minutes

Standard Time ≈ 13.92 minutes

Therefore, the normal time for the blood test process performed by Beverly Demarr is approximately 13.92 minutes, and the standard time for the blood test is approximately 14.04 minutes.

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To find the answer:

1. Remove parenthesis by multiplying the number outside parenthesis

Total = 125

P ( A and X )= 11/ total = 11/125= 0.088

P (B and X ) = 26/125 = 0.208

P (C l X ) = 6 /70 = 0.085

P (Bl Y) = 10/55 = 0.18

P (YlC)=12/55 =0.21

From least to greatest

0.085-0.088-0.18-0.208-0.21

P (C l X ) -P ( A and X -P (Bl Y))-P (B and X )-P (YlC)

The correct answer is c. Inferential Statistics.

Inferential statistics is the branch of statistics that allows for drawing conclusions about a population based on the information collected from a sample. When conducting research or surveys, it is often impractical or impossible to collect data from an entire population.

Instead, a representative sample is chosen, and inferential statistics are used to make inferences or predictions about the larger population. By analyzing the characteristics and patterns observed within the sample, inferential statistics enable researchers to make generalizations or draw conclusions about the population as a whole.

This process involves applying various statistical techniques, such as hypothesis testing and confidence intervals, to estimate population parameters and assess the reliability of the conclusions. Magnitude statistics, central tendency, and effect size are important concepts in statistics, but they do not specifically address the ability to draw population-level conclusions from sample data.

Magnitude statistics focuses on the size of the effect or relationship between variables, central tendency measures summarize the central values of a dataset, and effect size quantifies the strength of an effect or relationship.

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