Answers
Answer:
31. m∠E = 56.1°
32. c = 24.9 inches
Step-by-step explanation:
Question 31The Law of Sines relates the lengths of the sides of a triangle to the sines of its angles. It states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant for all three sides of the triangle.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Given values of triangle DEF:
m∠D = 81°d = 25e = 21To find m∠E, substitute the values into the Law of Sines formula and solve for E:
[tex]\dfrac{\sin D}{d}=\dfrac{\sin E}{e}[/tex]
[tex]\dfrac{\sin 81^{\circ}}{25}=\dfrac{\sin E}{21}[/tex]
[tex]\sin E=\dfrac{21\sin 81^{\circ}}{25}[/tex]
[tex]E=\sin^{-1}\left(\dfrac{21\sin 81^{\circ}}{25}\right)[/tex]
[tex]E=56.1^{\circ}\; \sf(nearest\;tenth)[/tex]
Therefore, the measure of angle E is 56.1°, to the nearest tenth.
See the attachment for the accurate drawing of triangle DEF.
[tex]\hrulefill[/tex]
Question 32The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
From inspection of triangle ABC:
C = 125°a = 13 inchesb = 15 inchesTo find the length of side c, substitute the values into the Law of Cosines formula and solve for c:
[tex]c^2=a^2+b^2-2ab \cos C[/tex]
[tex]c^2=13^2+15^2-2(13)(15) \cos 125^{\circ}[/tex]
[tex]c^2=169+225-390 \cos 125^{\circ}[/tex]
[tex]c^2=394-390 \cos 125^{\circ}[/tex]
[tex]c=\sqrt{394-390 \cos 125^{\circ}}[/tex]
[tex]c=24.8534667...[/tex]
[tex]c=24.9\; \sf inches\;(nearest\;tenth)[/tex]
Therefore, the length of side c is 24.9 inches, to the nearest tenth.
Related Questions
In order to compute a sample mean by hand, first the data values must be added up. Then the sum is divided by the
sample size.
x = xx
Given the data set below, compute the summation, identify the sample size, and calculate the sample mean.
19
10
15
17
16
a.) Ex =
b.) n =
c.) x =
Answers
a) The summation (Ex) of the given data set, we add up all the values
Ex = 77
b) n = 5
c) x = 15.4
a) To compute the summation (Ex) of the given data set, we add up all the values:
19 + 10 + 15 + 17 + 16 = 77
b) The sample size (n) is the total number of data points in the set. In this case, there are 5 data points, so:
n = 5
c) To calculate the sample mean (x), we divide the summation (Ex) by the sample size (n):
x = Ex / n
x = 77 / 5
x = 15.4
Therefore, the answers are:
a) Ex = 77
b) n = 5
c) x = 15.4
The summation is 77, the sample size is 5, and the sample mean is 15.4.
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For the sequence -27,-12, 3, 18,..., the expression that defines the nth term where a, = -27 is
Answers
Answer:
-27+15 (N-1)
Step-by-step explanation:
-27, -12, 3, 18
Take the second term and subtract the first term to find the common difference
-12 - (-27)
-12+27 = 15
The common difference is +15
We are adding 15 each time
The formula for an arithmetic sequence is
an = a1+d(n-1)
an = -27 +15(n-1)
Please answer ASAP I will brainlist
Answers
The resulting matrix after the rows are interchanged is given as follows:
[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]
How to obtain the resulting matrix?The matrix for this problem is defined as follows:
[tex]\left[\begin{array}{cccc}8&-2&1&7\\2&9&4&5\\1&4&-4&9\end{array}\right][/tex]
The row 1 is given as follows:
[8 -2 1 7].
The row 2 is given as follows:
[2 9 4 5].
Interchanging the rows means that the elements of the row 1 in the matrix is exchanged with the elements of row 2, hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]
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If the mean of a negatively skewed distribution is 122, which of these values could be the median of the distribution
Answers
118 be the median of a positively skewed distribution with a mean of 122. Option D.
To determine which of the given values could be the median of a positively skewed distribution with a mean of 122, we need to consider the relationship between the mean, median, and skewness of a distribution.
In a positively skewed distribution, the tail of the distribution is stretched towards higher values, meaning that there are more extreme values on the right side. Consequently, the median, which represents the value that divides the distribution into two equal halves, will typically be less than the mean in a positively skewed distribution.
Let's examine the given values in relation to the mean:
A. 122: This value could be the median if the distribution is perfectly symmetrical, but since the distribution is positively skewed, the median is expected to be less than the mean. Thus, 122 is less likely to be the median.
B. 126: This value is higher than the mean, and since the distribution is positively skewed, it is unlikely to be the median. The median is expected to be lower than the mean.
C. 130: Similar to option B, this value is higher than the mean and is unlikely to be the median. The median is expected to be lower than the mean.
D. 118: This value is lower than the mean, which is consistent with a positively skewed distribution. In such a distribution, the median is expected to be less than the mean, so 118 is a plausible value for the median.
In summary, among the given options, (118) is the most likely value to be the median of a positively skewed distribution with a mean of 122. So Option D is correct.
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Note the complete question is
If the mean of a positively skewed distribution is 122, which of these values could be the median of the distribution?
A. 122
B. 126
C. 130
D. 118
For a recent year, 52.7 million people participated in recreational boating. Sixteen years later, that number increased to 57.3
million. Determine the percent increase. Round to one decimal place.
The percent increase was approximately
%.
Answers
The percent increase in recreational boating participation over the sixteen-year period is approximately 8.72%. This means that the number of participants increased by around 8.72% from 52.7 million to 57.3 million.
To determine the percent increase in recreational boating participation over the sixteen-year period, we can use the following formula:
Percent Increase = ((New Value - Old Value) / Old Value) * 100
Using the given information, we have an old value of 52.7 million and a new value of 57.3 million.
Percent Increase = ((57.3 million - 52.7 million) / 52.7 million) * 100
= (4.6 million / 52.7 million) * 100
= 0.0872 * 100
= 8.72%
This increase indicates a positive trend in recreational boating, reflecting a growing interest in this activity over time. Factors such as improved accessibility, marketing efforts, and increasing disposable income may have contributed to this upward trend.
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PLSPLSS PLSSMSL HELP ME
Answers
Answer:
1. x = 18
2. x = 31
Step-by-step explanation:
1. Angles in a quadrilateral sum to 360°.
360 -(60 +130 +70) = 360 -260 = 100
So, x +82 = 100. x = 100 -82 = 18
2. Angles in a triangle sum to 180°. 180 -(29 +75) = 180 -104 = 76.
So, -17 +3x = 76. 3x = 93. x = 93/3 = 31
Use a Calculator to evaluate The following. Round the answer to the nearest hundredths
1. Cos 10
2. Sin 30
3. Sin 20
4. Tan 25
5. Tan 48.5
Answers
1. Using a calculator, we find that cos 10 ≈ 0.98.
2. Using a calculator, we find that sin 30 ≈ 0.50.
3. Using a calculator, we find that sin 20 ≈ 0.34.
4. Using a calculator, we find that tan 25 ≈ 0.47.
5. Using a calculator, we find that tan 48.5 ≈ 1.14.
Using a calculator to evaluate the given trigonometric functions, rounded to the nearest hundredth, we have:
Cos 10:
Using a calculator, we find that cos 10 ≈ 0.98.
Sin 30:
Using a calculator, we find that sin 30 ≈ 0.50.
Sin 20:
Using a calculator, we find that sin 20 ≈ 0.34.
Tan 25:
Using a calculator, we find that tan 25 ≈ 0.47.
Tan 48.5:
Using a calculator, we find that tan 48.5 ≈ 1.14.
These values represent the approximate decimal values of the trigonometric functions at the given angles, rounded to the nearest hundredth.
Just a reminder, when using a calculator, make sure it is set to the correct angle mode (degrees or radians) as per the given problem.
It's important to note that these values are approximate since they are rounded to the nearest hundredth. If you need more precise values, you can use a calculator that allows for a greater number of decimal places or use trigonometric tables.
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a spinner with 10 equally sized slices 4 yellow, 4 red, 2 blue. probability that the dial stops on yellow?
Answers
The probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
To find the probability that the spinner stops on yellow, we need to determine the number of favorable outcomes (yellow) and the total number of possible outcomes.
The spinner has 10 equally sized slices, with 4 yellow, 4 red, and 2 blue.
The number of favorable outcomes (yellow) is 4 because there are 4 yellow slices.
The total number of possible outcomes is 10 because there are 10 slices in total.
Therefore, the probability of the spinner stopping on yellow can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 10
Simplifying this fraction, we get:
Probability = 2 / 5
So, the probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
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what is the value of m
Answers
Answer:
114°--------------------------
Angle G is central angle and angle E is inscribed angle, both with same endpoints.
According to the inscribed angle theorem the inscribed angle is half of the central angle.
Hence the central angle G measures:
m∠G = 2(m∠E)m∠G = 2(57°)m∠G = 114°Does anybody know the answer i need. It quick!!!!!
Answers
The area of the obtuse triangle is 34 square feet with a base of 10 ft and height of 6.8 ft.
To find the area of the obtuse triangle, we can use the formula A = (1/2) * base * height. Let's denote the unknown part of the base as x.
In the given triangle, we have the width of the obtuse angle triangle as 10 ft, the height (perpendicular) as 6.8 ft, and the unknown part of the base as x.
Using the formula, we can calculate the area as:
A = (1/2) * (10 + x) * 6.8
Simplifying this expression, we get:
A = 3.4(10 + x)
Now, we need to determine the value of x. From the given information, we know that the width of the obtuse angle triangle is 10 ft. This means the sum of the two parts of the base is 10 ft. Therefore, we can write the equation:
x + 10 = 10
Solving for x, we find:
x = 0
Since x = 0, it means that one part of the base has a length of 0 ft. Therefore, the entire base is formed by the width of the obtuse angle triangle, which is 10 ft.
Now, substituting this value of x back into the area formula, we have:
A = 3.4(10 + 0)
A = 3.4 * 10
A = 34 square feet
Hence, the area of the obtuse triangle is 34 square feet.
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What 2 numbers can multiply to -40 and add up to 6
Answers
Answer: 10 and -4
Step-by-step explanation: 10 + - 4 = 6 and 10 x -4 = -40
If sin(x+y)= 1/2(sin x) + square root of 3/2(cos x), what is the value of y
Answers
Answer:
y = π/3
Step-by-step explanation:
To find the value of y, we can use the trigonometric identity for the sum of angles:
sin(x + y) = sin x * cos y + cos x * sin y
Comparing this with the given equation:
sin(x + y) = 1/2(sin x) + √3/2(cos x)
We can equate the corresponding terms:
sin x * cos y = 1/2(sin x) ----(1)
cos x * sin y = √3/2(cos x) ----(2)
From equation (1), we can see that cos y = 1/2.
From equation (2), we can see that sin y = √3/2.
To determine the values of y, we can use the trigonometric values of cosine and sine in the first quadrant of the unit circle.
In the first quadrant, cos y is positive, so cos y = 1/2 corresponds to y = π/3 (60 degrees).
Similarly, sin y is positive, so sin y = √3/2 corresponds to y = π/3 (60 degrees).
Therefore, the value of y is y = π/3 (or 60 degrees).
(a) Un ángulo mide 47°. ¿Cuál es la medida de su complemento?
(b) Un ángulo mide 149°. ¿Cuál es la medida de su suplemento?
Answers
El supplemento y el complemento de cada ángulo son, respectivamente:
Caso A: m ∠ A' = 43°
Caso B: m ∠ A' = 31°
¿Cómo determinar el complemento y el suplemento de un ángulo?De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:
Ángulo y su complemento
m ∠ A + m ∠ A' = 90°
Ángulo y su suplemento
m ∠ A + m ∠ A' = 90°
Donde:
m ∠ A - Ángulom ∠ A' - Complemento / Suplemento.Ahora procedemos a determinar cada ángulo faltante:
Caso A: Complemento
47° + m ∠ A' = 90°
m ∠ A' = 43°
Caso B: Suplemento
149° + m ∠ A' = 180°
m ∠ A' = 31°
ObservaciónEl enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.
The statement is written in Spanish and its answer is written in the same language.
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true or false euclidean geometry is geometry on a sphere
Answers
Answer: False
Step-by-step explanation:
Spherical geometry, on the other hand, is a type of non-Euclidean geometry that is specifically concerned with studying the properties of curved surfaces, such as spheres.
Hope this help! Have a good day!
please help quick
Which of the following are solutions to the quadratic equation? Check all that
apply.
Answers
The solutions to the quadratic equation 2x² + 6x - 10 = x² + 6 are -8 and 2.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
2x² + 6x - 10 = x² + 6
First, reorder the quadratic equation in standard form:
2x² + 6x - 10 = x² + 6
2x² - x² + 6x - 10 - 6 = x² - x² + 6 - 6
2x² - x² + 6x - 10 - 6 = 0
x² + 6x - 10 - 6 = 0
x² + 6x - 16 = 0
Next, factor the equation using the AC method:
( x - 2 )( x + 8 ) = 0
Equate each factor to 0 and solve for x:
( x - 2 ) = 0
x - 2 = 0
x = 2
( x + 8 ) = 0
x + 8 = 0
x = -8
Therefore, the solutions are -8 and 2.
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Evaluate the given expression for x=5
Answers
x² + 3x - 2
(5)² + 3 × 5- 2
25 + 15 - 2
40 - 2
38...
Pls help I need help on this
Answers
Answer:
[tex]5a2b2/4[/tex]
Step-by-step explanation:
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
Answers
Given the information in the diagram, the theorem that best justifies why lines j and k must be parallel include the following: D. converse alternate exterior angles theorem.
What are parallel lines?In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.
In Mathematics and Geometry, the alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.
Since the alternate exterior angles are congruent, we can logically deduce the following based on the converse alternate exterior angles theorem;
93° ≅ 93° (lines j and k are parallel lines).
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Complete Question:
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
alternate interior angles theorem
alternate exterior angles theorem
converse alternate interior angles theorem
converse alternate exterior angles theorem
Which is equivalent to 4/9 1/2x*?
92x
9 1/8x
Answers
Answer:
B. [tex] 9^{\frac{1}{8}x} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{9}^{\frac{1}{2}x} = [/tex]
[tex] = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{4} \times \frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{8}x} [/tex]
MLMS4 Day 3 (1 hour) SBA Task: Project November 2023 Which sides of the rectangle (that formed the sides of the cylinder) has the same length as the circumference of the circles? Which sides of the rectangle has the same length of the height of the cylinder. What do you notice between your model and the practical calculation.
Answers
The sides of the rectangle that have the same length as the circumference of the circles are the sides parallel to the bases of the cylinder. The sides of the rectangle that have the same length as the height of the cylinder are the sides perpendicular to the bases. While the model provides a simplified representation, practical calculations might have slight differences due to real-world factors.
In a cylinder, the two circular bases are connected by a curved surface, forming a three-dimensional shape. The rectangular shape that wraps around the curved surface of the cylinder is called the lateral surface or the lateral area.
To determine which sides of the rectangle have the same length as the circumference of the circles, we need to understand the geometry of a cylinder. The circumference of a circle is calculated using the formula:
Circumference = 2πr,
where r is the radius of the circle. In a cylinder, the bases are identical circles, so the circumference of each base is equal. Therefore, the sides of the rectangle that are parallel to the bases have the same length as the circumference of the circles.
Now, let's consider the height of the cylinder. The height is the distance between the two bases and is perpendicular to the bases. In the rectangular representation of the cylinder, the sides that are perpendicular to the bases represent the height. Hence, the sides of the rectangle that are perpendicular to the bases have the same length as the height of the cylinder.
When comparing the model (rectangular representation) with practical calculations, we may notice some differences. The model provides a simplified representation of the cylinder, assuming that the lateral surface is perfectly wrapped around the curved surface. However, in practical calculations, there might be slight variations due to factors like material thickness, manufacturing processes, or measuring precision. These variations can result in minor deviations between the model and the practical calculations.
It's important to consider that the model is an approximation and serves as a visual aid to understand the basic properties of the cylinder. In real-life applications or engineering calculations, precise measurements and considerations of tolerances are crucial.
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Write the correct measurement for A-F (Example 2.2, 5.9, 9)
Answers
Answer:
9
Step-by-step explanation:
The average student loan debt for college graduates is $25,200. Suppose that that distribution is normal and that the standard deviation is $11,200. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar.
a. What is the distribution of X? X - N
b Find the probability that the college graduate has between $27,250 and $43,650 in student loan debt
c. The middle 20% of college graduates loan debt lies between what two numbers? Low: $ High: $
Answers
a) The distribution of X, the student loan debt of a randomly selected college graduate, is normal with a mean of $25,200 and a standard deviation of $11,200. b) The probability is approximately 7.28%.
c) The middle lies between approximately $22,164 and $28,536.
How to Find Probability?a. The distribution of X, the student loan debt of a randomly selected college graduate, is a normal distribution (bell-shaped curve) with a mean (μ) of $25,200 and a standard deviation (σ) of $11,200. We can represent this as X ~ N(25200, 11200).
b. To find the probability that the college graduate has between $27,250 and $43,650 in student loan debt, we need to calculate the z-scores for these two values and then find the area under the normal curve between those z-scores.
First, we calculate the z-score for $27,250:
z1 = (X1 - μ) / σ = (27250 - 25200) / 11200 ≈ 1.8304
Next, we calculate the z-score for $43,650:
z2 = (X2 - μ) / σ = (43650 - 25200) / 11200 ≈ 1.6518
Now, we need to find the area under the normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area.
Using a standard normal distribution table or a calculator, the probability is approximately P(1.6518 ≤ Z ≤ 1.8304) ≈ 0.0728.
c. To find the middle 20% of college graduates' loan debt, we need to find the range of values that contain the central 20% of the distribution. This range corresponds to the values between the lower and upper percentiles.
The lower percentile is the 40th percentile (50% - 20%/2 = 40%) and the upper percentile is the 60th percentile (50% + 20%/2 = 60%).
Using a standard normal distribution table or a calculator, we can find the z-scores corresponding to these percentiles:
For the lower percentile (40th percentile):
z_lower = invNorm(0.40) ≈ -0.2533
For the upper percentile (60th percentile):
z_upper = invNorm(0.60) ≈ 0.2533
Now, we can convert these z-scores back to the corresponding loan debt values:
Lower debt value:
X_lower = μ + z_lower * σ = 25200 + (-0.2533) * 11200 ≈ $22,164
Upper debt value:
X_upper = μ + z_upper * σ = 25200 + 0.2533 * 11200 ≈ $28,536
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Choose the justification for each step of the given equation. -6=-2/3(x+12)+1/3x
Answers
The steps used in the solution of the equation -6 = -2/3(x + 12) + 1/3x are based on the principles of the Distributive Property, combining like terms, addition property of equality, symmetric property, subtraction property of equality, and multiplication property of equality.
Let's analyze the steps of the solution for the given equation -6 = -2/3(x + 12) + 1/3x:
Step 1: Distributive Property
The equation begins with the Distributive Property, which states that you can distribute a factor to each term inside parentheses. In this case, we distribute -2/3 to (x + 12), resulting in -2/3 * x and -2/3 * 12.
Step 2: Simplification
We simplify the expression -2/3 * 12 to -8, as multiplying -2/3 by 12 gives us -24, and simplifying the fraction -24/3 yields -8.
Step 3: Combine Like Terms
We combine the like terms -2/3x and -8. The equation becomes -2/3x - 8 + 1/3x.
Step 4: Combine Like Terms
We combine the like terms -2/3x and 1/3x by adding their coefficients. The sum of -2/3x and 1/3x is -1/3x.
Step 5: Addition Property of Equality
We add -1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 - 1/3x = -1/3x.
Step 6: Symmetric Property
Since the equation has a form of -1/3x = -6 - 1/3x, we can rearrange the terms using the Symmetric Property.
Step 7: Addition Property of Equality
We add 1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 = 0.
Step 8: Subtraction Property of Equality
We subtract 0 from both sides of the equation to simplify it further. The equation remains -6 = 0.
Step 9: Multiplication Property of Equality
We multiply both sides of the equation by any non-zero number to check for consistency. In this case, there is no need for multiplication as the equation is already in its simplified form.
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Please help me solve this
Answers
Answer:
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
Answer:
Third option
Step-by-step explanation:
-3(2x - 5) < 5(2 - x)
-6x + 15 < 10 - 5x <-- Third option
15 < 10 + x
5 < x
x > 5
There only appears to be one option. The solution to the inequality is x>5, not x<5.
Solve it for me please
Answers
1a.) The amount that the eldest son received would be =GHç 1,360
b .) The amount received by the daughter would be =G Hç 2176
c.) The difference between the amount the two sons received would be =GHç1,904
How to calculate the amount received by the eldest son?For 1a.)
The amount that the land is worth= $8,600
The amount received for various purposes= $1,800
The remaining amount shared to the sons= 8,600-1800= $6,800
The percentage amount received by the eldest son= 20% of 6800
That is;
= 20/100×6800/1
= 136000/100
= $1,360
The remaining amount= 6800-1360= $5,440
For 1b.)
The ratio that the remaining amount was shared between the other son and the daughter = 3 : 2 respectively.
The total ratio= 3+2=5
For daughter= 2/5× 5440
= 10880/5 = 2176
The other son= 5440-2176 = 3264
For 1c.)
The difference between the amount the two sons received would be =3264-1,360 = GHç1,904.
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I WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
In a randomized block design blocked by gender, treatments should be assigned randomly within each gender block. The correct assignment maintains a distribution of one treatment for each gender. Looking at the given options, only one meets this criterion:
OA: (1f, 2f), B: (1m, 2m). C: (3f, 3m). D: (4f, 4m)
Each treatment group A, B, C, and D contains one male and one female, making the distribution of treatments blocked by gender.
Two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2030 through 2035, with t = 0 corresponding to 2030.
R1 = 7.23 + 0.25t + 0.03t^2
R2 = 7.23 + 0.1t + 0.01t^2
How much more total revenue (in millions of dollars) does that model project over the six-year period ending at t = 5? (Round your answer to three decimal places.)
Answers
Step-by-step explanation:
To find the difference in total revenue projected by the two models over the six-year period ending at t = 5, we need to calculate the revenue for each model from t = 0 to t = 5 and subtract the results.
For R1:
R1 = 7.23 + 0.25t + 0.03t^2
Substituting t = 5:
R1(5) = 7.23 + 0.25(5) + 0.03(5^2)
R1(5) = 7.23 + 1.25 + 0.75
R1(5) = 9.23 + 0.75
R1(5) = 9.98 million dollars
For R2:
R2 = 7.23 + 0.1t + 0.01t^2
Substituting t = 5:
R2(5) = 7.23 + 0.1(5) + 0.01(5^2)
R2(5) = 7.23 + 0.5 + 0.25
R2(5) = 7.73 + 0.25
R2(5) = 7.98 million dollars
To find the difference, we subtract R2(5) from R1(5):
Difference = R1(5) - R2(5)
Difference = 9.98 - 7.98
Difference = 2 million dollars
Therefore, the model R1 projects 2 million dollars more in total revenue than R2 over the six-year period ending at t = 5.
For R1:
R1 = 7.23 + 0.25t + 0.03t^2
Substituting t = 5 into the equation:
R1 = 7.23 + 0.25(5) + 0.03(5^2)
R1 = 7.23 + 1.25 + 0.75
R1 = 9.23 + 0.75
R1 = 9.98 million dollars
For R2:
R2 = 7.23 + 0.1t + 0.01t^2
Substituting t = 5 into the equation:
R2 = 7.23 + 0.1(5) + 0.01(5^2)
R2 = 7.23 + 0.5 + 0.25
R2 = 7.73 + 0.25
R2 = 7.98 million dollars
To find the difference in total revenue, we subtract R2 from R1:
Difference = R1 - R2
Difference = 9.98 - 7.98
Difference = 2 million dollars
Therefore, the model R1 projects $2 million more in total revenue over the six-year period ending at t = 5 compared to model R2.
The expression
28 (78-14)9-13(78-49)9
can be
rewritten as
(X-y)" (262 + y? + gxy). Whatis the value of p?
Answers
Answer:
p =1 0
Step-by-step explanation:
x³(x - y)⁹ - y³(x - y)⁹ = (x - y)⁹[x³ - y³]
= (x - y)⁹(x - y)(x² + y² + xy)
= (x - y)¹⁰(x² + y² + xy)
where p = 10 and q = 1
Answer:
p = 10
Step-by-step explanation:
Given expression:
[tex]x^3(x-y)^9 - y^3(x-y)^9[/tex]
Factor out the common term (x - y)⁹:
[tex](x-y)^9(x^3- y^3)[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of two cubes}\\\\$x^3-y^3=(x-y)(x^2+y^2+xy)$\\\end{minipage}}[/tex]
Rewrite the second parentheses as the difference of two cubes.
[tex](x-y)^9(x-y)(x^2+y^2+xy)[/tex]
[tex]\textsf{Apply\:the\:exponent\:rule:} \quad a^b\cdot \:a^c=a^{b+c}[/tex]
[tex](x-y)^{9+1}(x^2+y^2+xy)[/tex]
[tex](x-y)^{10}(x^2+y^2+xy)[/tex]
Comparing the rewritten original expression with the given expression:
[tex](x-y)^{10}(x^2+y^2+xy)=(x-y)^p(x^2+y^2+qxy)[/tex]
We can see that [tex](x-y)^p[/tex] corresponds to [tex](x-y)^{10}[/tex] in the given expression.
Therefore, we can conclude that p = 10.
Given the following equation of a line x+6y= 3, determine the slope of a line that is perpendicular.
Answers
The slope of a line that is perpendicular to the given line x + 6y = 3 is 6.
To determine the slope of a line that is perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.
The equation of the given line is x + 6y = 3.
To find the slope of the given line, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:
x + 6y = 3
6y = -x + 3
y = (-1/6)x + 1/2
From the equation y = (-1/6)x + 1/2, we can see that the slope of the given line is -1/6.
To find the slope of a line that is perpendicular, we take the negative reciprocal of -1/6.
The negative reciprocal of -1/6 can be found by flipping the fraction and changing its sign:
Negative reciprocal of -1/6 = -1 / (-1/6) = -1 * (-6/1) = 6
Therefore, the slope of a line that is perpendicular to the given line x + 6y = 3 is 6.
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