These expressions are not equivalent because the coefficients of x have different signs (-1/8x vs. 1/8x).
To determine if the expressions 1/2x + 3/4 - 5/8x - 7/8 and 1/8(x + 1) are equivalent, we can simplify both expressions and compare the results.
Let's start with the first expression:
1/2x + 3/4 - 5/8x - 7/8
First, we need to combine like terms.
The x terms are 1/2x and -5/8x.
To combine them, we find a common denominator, which is 8:
1/2x - 5/8x = (4/8)x - (5/8)x = (4 - 5)/8x = -1/8x
Now, let's combine the constant terms, which are 3/4 and -7/8:
3/4 - 7/8 = (6/8) - (7/8) = -1/8
Combining both parts, we get:
-1/8x - 1/8
Now, let's simplify the second expression:
1/8(x + 1)
Distributing 1/8 to the terms inside the parentheses, we have:
1/8 [tex]\times[/tex] x + 1/8 [tex]\times[/tex] 1 = 1/8x + 1/8
Comparing the simplified expressions, we have:
-1/8x - 1/8 = 1/8x + 1/8
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A one-kilogram cake is divided into 3 pieces whose weights are in the ratio 1:2:4. What is the weight of the second piece?
EXPLANATION ALONG WITH ANSWER NEEDED. Wrong answers and answers without explanation- will be reported.
Considering the ratio provided for cake pieces, the weight of the second piece of the cake is 2/7 kilograms.
Given that a one-kilogram cake is divided into 3 pieces whose weights are in the ratio 1:2:4.
We have to find the weight of the second piece.
Steps to find the weight of the second piece
Step 1: Let the three parts of the cake be x, 2x, and 4x respectively, where x is the weight of the first part of the cake.
Step 2: Find the total weight of the cake:
x + 2x + 4x = 7x
Total weight of cake = 7x
Total weight of cake = 1kg
Therefore,
7x = 1 kg
Or x = 1 / 7 kg.
Step 3: Find the weight of the second part of the cake (2x):
Weight of the second part of the cake = 2x
= 2 × (1 / 7)
= 2 / 7 kg.
Weight of the second part of the cake is 2/7 kilograms.
To conclude, the weight of the second piece of the cake is 2/7 kilograms.
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The following shape has 1 pair of parallel sidesWhat is the area of the shape?
It is not possible to determine the area of the shape from the given information as the measurements of the sides and angles are not provided.
However, we can identify the shape as a trapezoid because it has one pair of parallel sides. A trapezoid is a quadrilateral with one pair of parallel sides. To calculate the area of a trapezoid, we can use the formula:Area of trapezoid = 1/2 × (sum of parallel sides) × (distance between parallel sides)If we have the measurements of the parallel sides and the distance between them, we can substitute them into the formula to find the area of the trapezoid.
If the measurements are not provided, we cannot find the area of the trapezoid. Thus, it is not possible to determine the area of the shape from the given information, which only tells us that it has one pair of parallel sides.
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The given figure has only one pair of parallel sides. The opposite sides of the trapezium are not parallel. The formula to calculate the area of the trapezium is given as:
A = (a+b)/2 * h, where 'a' and 'b' are the parallel sides of the trapezium and 'h' is the distance between these parallel sides.
We can clearly see that the parallel sides 'a' and 'b' are 6 cm and 10 cm, respectively, and the height 'h' of the trapezium is 4 cm.
Therefore, substituting these values in the above formula, we have:
A = (6 + 10)/2 * 4A = 16/2 * 4A = 8 * 4A
= 32The area of the trapezium is 32 sq cm.
Thus, the area of the given shape is 32 square centimeters.
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Simplify this numerical expression using the order of operations. 5. 75 - 1 2 (20 ÷ 2. 5) ÷ 2 6 Order of Operations: 1. Evaluate within parentheses. 2. Evaluate exponents. 3. Multiply and divide from left to right. 4. Add and subtract from left to right. What is the value of the expression?.
The value of the given expression is approximately 71.31.
[tex]$$75 - 12(20 ÷ 2.5) ÷ 26$$[/tex]
The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.
So, we follow the Order of Operations to solve this expression.
Firstly, we will evaluate the parentheses:
[tex]$$20 ÷ 2.5 = 8$$[/tex]
Now, the given expression becomes:
[tex]$$75 - 12 × 8 ÷ 26$$[/tex]
Then, we will evaluate multiplication and division in order from left to right.
12 × 8 = 96
So, the given expression becomes:
[tex]$$75 - 96 ÷ 26$$[/tex]
Evaluating division, we get:
[tex]$$75 - 3.6923$$[/tex]
Now, we will add and subtract from left to right.
[tex]75 − 3.6923 ≈ 71.31[/tex]
Therefore, the value of the given expression is approximately 71.31.
So, the required is approximately 71.31.
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Wallace works at the Computer Wholesale Warehouse, where he develops visual impressions of products for advertisements and marketing materials. What type of work does Wallace perform
The required, Wallace performs graphic design work at the Computer Wholesale Warehouse.
Based on the description provided, Wallace performs visual design or graphic design work at the Computer Wholesale Warehouse. He develops visual impressions of products for advertisements and marketing materials. This involves creating visual elements, such as graphics, images, and layouts, to effectively convey messages and promote products.
Wallace's role at the Computer Wholesale Warehouse involves performing visual design work to create captivating visual impressions of products for advertisements and marketing materials, contributing to the overall effectiveness of their promotional efforts.
Thus, the required, Wallace performs graphic design work at the Computer Wholesale Warehouse.
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Tre is helping his mom buy soil and plants for her small garden. Soil costs $3 per bag and plants
cost $12 each. Tre's mom wants at least 5 plants in her garden, but Tre can spend no more than $120.
Write a System Of Inequalities and Write Two Possible Solutions
The System Of Inequalities are : $3s + $12p ≤ $120
How to Write a System Of Inequalities and Write Two Possible SolutionsLet's represent the number of bags of soil as 's' and the number of plants as 'p'.
The given information can be translated into the following system of inequalities:
1. Cost inequality: $3s + $12p ≤ $120
(The total cost of soil bags and plants should be less than or equal to $120.)
2. Plant requirement: p ≥ 5
(Tre's mom wants at least 5 plants in her garden.)
Now, let's find two possible solutions that satisfy the given conditions:
Solution 1:
- Let's consider Tre purchasing 8 bags of soil (s = 8).
- Then, he can buy 5 plants (p = 5).
(8 bags of soil cost $24, and 5 plants cost $60, which sums up to $84.)
Solution 2:
- Let's consider Tre purchasing 10 bags of soil (s = 10).
- Then, he can buy 6 plants (p = 6).
(10 bags of soil cost $30, and 6 plants cost $72, which sums up to $102.)
These two solutions satisfy the conditions of at least 5 plants and a total cost of $120 or less.
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A rectangular box has width (x), length (5x - 1), and height (2x + 3). The area is 29,946 in. Find X
I need help please
To find the value of x in the given problem, we can start by calculating the area of the rectangular box. The area of a rectangular box is given by the formula A = 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height. In this case, the area is given as 29,946 in².
The first step is to substitute the given values into the formula:
29,946 = 2(x)(5x - 1) + 2(x)(2x + 3) + 2(5x - 1)(2x + 3).
Next, we simplify the equation and distribute the terms:
29,946 = 2(5x² - x) + 2(2x² + 3x) + 2(10x² + 15x - 2x - 3).
After combining like terms, we have:
29,946 = 10x² - 2x + 4x² + 6x + 20x² + 30x - 4x - 6.
Combining similar terms further, we get:
29,946 = 34x² + 40x - 6.
Now, we can rearrange the equation and set it equal to zero:
34x² + 40x - 29,946 = 0.
To solve this quadratic equation, we can either factor it or use the quadratic formula. However, since the equation is not easily factorable, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a).
By substituting the values a = 34, b = 40, and c = -29,946 into the quadratic formula, we can find the two possible values of x. However, since we are looking for a real-world length, we can discard any negative or non-real solutions.
After solving the equation, we find that x is approximately equal to 24.4 or x ≈ -29.36. Since negative values are not meaningful in the context of length, we can conclude that the value of x for which the rectangular box has the given area of 29,946 in² is approximately 24.4 inches.
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Lincoln's monthly bank statement showed the following deposits and withdrawals: − −$28. 51, − −$41. 34, $90. 95, − −$88. 95, $11. 16 If Lincoln's balance in the account was $19. 96 at the beginning of the month, what was the account balance at the end of the month?
After considering the deposits and withdrawals, the account balance at the end of the month is $64.23.
To calculate the account balance at the end of the month, we need to add up all the deposits and withdrawals. The negative values represent withdrawals, while the positive values represent deposits.
Starting with an initial balance of $19.96, we can calculate the final balance by adding the amounts of the deposits and subtracting the amounts of the withdrawals.
Starting balance: $19.96
Deposits: $90.95, $11.16
Withdrawals: -$28.51, -$41.34, -$88.95
Adding the deposits: $19.96 + $90.95 + $11.16 = $122.07
Subtracting the withdrawals: $122.07 - $28.51 - $41.34 - $88.95 = $64.23
Therefore, the account balance at the end of the month is $64.23.
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Given \small \Delta ABC\sim\Delta DEC, could you use the proportion \small \frac{9}{10}=\frac{8.75}{EC} to determine the measure of EC? If yes, type yes and solve for EC. (Must type yes and give value of EC) If no, type no and rewrite the proportion and then solve for EC. (Must type no, give the correct proportion, and the value of EC)
Yes, In order to determine the measure of EC, we need a proportion that relates the corresponding sides of similar triangles. we can use the proportion 9/10 = 8.75/EC to determine the measure of EC
The proportion is,
To solve for EC, we can cross-multiply and then solve for EC.
9/10 = 8.75/EC
9×EC=10×8.75
Simplifying we get,
EC = 9.72
Therefore, the measure of EC is approximately 9.72 units.
Please provide the correct proportion relating the corresponding sides of
ΔABC and ΔDEC, and I'll be happy to help you solve for EC.
Hence, the correct answer is:Yes, EC ≈ 9.7222.
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find the side of the triangle if two of its sides are equal the third side is 1 1/3 cm longer than the others and its perimeter is 5 2/5cm
The lengths of the sides of the triangle are approximately:
The two equal sides: 61/45 cm
The third side: 1089/405 cm
Let's assume that the two equal sides of the triangle are represented by "x" cm each. According to the given information, the third side is 1 1/3 cm longer than the other two sides.
So, the length of the third side can be represented as "x + 1 1/3" cm.
The perimeter of a triangle is the sum of all its sides. In this case, the perimeter is given as 5 2/5 cm.
Using this information, we can write the equation:
2x + (x + 1 1/3) = 5 2/5
To solve this equation, let's convert the mixed number 1 1/3 to an improper fraction.
1 1/3 = (3× 1 + 1) / 3 = 4/3
Substituting the value, we have:
2x + (x + 4/3) = 5 2/5
To simplify the equation, let's convert the mixed number 5 2/5 to an improper fraction.
5 2/5 = (5 ×5 + 2) / 5 = 27/5
Now, the equation becomes:
2x + (x + 4/3) = 27/5
Combining like terms, we have:
3x + 4/3 = 27/5
To eliminate the fractions, let's multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 15:
15 × (3x + 4/3) = 15 ×(27/5)
45x + 20 = 81
Subtracting 20 from both sides:
45x = 61
Dividing both sides by 45:
x = 61/45
So, the value of x is 61/45 cm. This represents the length of the two equal sides of the triangle.
Now, to find the length of the third side, we substitute x back into the expression:
x + 1 1/3 = (61/45) + 4/3
To add these fractions, we need to find a common denominator. The LCM of 45 and 3 is 45:
[(61/45) × (3/3)] + (4/3) = (183/135) + (4/3)
Now, we can add the fractions:
(183/135) + (4/3) = (549/405) + (540/405) = 1089/405
So, the length of the third side is 1089/405 cm.
Therefore, the lengths of the sides of the triangle are approximately:
The two equal sides: 61/45 cm
The third side: 1089/405 cm
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In the funtion f(x)=1/x which of these could be a value of f(x) when x is close to zero
In the function f(x) = 1/x, when x is close to zero, the value of f(x) approaches positive or negative infinity. As x approaches zero from the positive side (x → 0+).
The function f(x) = 1/x becomes increasingly large and approaches positive infinity. This is because dividing a positive number by a very small positive number yields a very large positive result.
On the other hand, as x approaches zero from the negative side (x → 0-), the function f(x) = 1/x also becomes increasingly large but in the negative direction, approaching negative infinity. Dividing a negative number by a very small negative number yields a very large negative result.
However, it is important to note that the function f(x) = 1/x is undefined at x = 0 since division by zero is undefined in mathematics. Therefore, we say that the function has a vertical asymptote at x = 0, meaning that the function gets arbitrarily close to positive or negative infinity as x approaches zero, but it never actually reaches zero. In conclusion, when x is close to zero in the function f(x) = 1/x, the value of f(x) could be positive or negative infinity depending on whether x approaches zero from the positive or negative side, respectively.
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Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. His Revenue is given by the function R - $62p, where Cis the total cost
per month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. How many pets must he groom each month
to break even?
Jordan's pet grooming business has a monthly cost function of C - $12p+ $2100. The monthly cost function for Jordan's pet-grooming company is C - $12p+ $2100.
His Revenue is given by the function R - $62p, where C is the total costper month, R is the total revenue he receives each month and x is the number of pets he grooms in a month. We need to find out how many pets must he groom each month to break even.Let's set revenue equal to costs, and solve for p.R = C62p = 12p + 2100p = (12p + 2100) / 62p = 0.1935p ≈ 19.35 petsJordan must groom approximately 19.35 pets each month to break even. The nearest whole number is 19.
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A scooter rental store charges a $4 rental fee plus $1. 50 for each hour a scooter is rented. What are the slope and y- intercept that represent this situation
Answer:
y = 1.5x + 4
The slope is 1.5, and the y-intercept is 4.
An 85kg man stands on a scale inside an elevator. What is the weight in Newtons that the scale reads when the elevator is
a. at rest?
b. moving upward at a constant speed of 5m/s?
c. moving downward at a constant speed of 8m/s?
d. moving with an upward acceleration of 3 m/s2
e. moving with a downward acceleration of 4 m/s2
The weight in Newtons that the scale reads when the elevator is in different scenarios can be calculated using the formula W = mg, where W = weight, m= mass, and g = the acceleration due to gravity.
a. When the elevator is at rest, there is no acceleration, so the weight will be equal to the gravitational force acting on the person. The weight can be calculated as W = mg, where m is the mass of the person (85 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the weight is W = 85 kg * 9.8 m/s^2.
b. the weight will remain the same as the gravitational force, which is calculated using the formula W = mg. c. The acceleration is still zero, and the weight will be the same as the gravitational force, calculated using the formula W = mg.
d. We need to consider the net force acting on the person. The net force will be the sum of the gravitational force and the force due to the acceleration. The weight can be calculated as W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration (3 m/s^2).
e. We calculate the weight similarly to case d. The weight is W = mg + ma, where m is the mass of the person (85 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the downward acceleration (-4 m/s^2) since it acts in the opposite direction.
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Nicholas scoops a few gumballs into his bag. When he weighs it, he finds that he scooped 0.76 pounds.
Nicholas scooped a few gumballs into his bag and found that it weighed 0.76 pounds.
Nicholas's bag of gumballs weighs 0.76 pounds. This weight includes the combined mass of the gumballs and the bag itself. The weight measurement indicates the force exerted by the bag due to the gravitational pull of the Earth. To determine the weight of just the gumballs, Nicholas would need to subtract the weight of the bag from the total weight.
To find the weight of the bag, Nicholas could use a scale or balance to measure an empty bag of the same type. Once he knows the weight of the empty bag, he can subtract that weight from the total weight of the bag with the gumballs. The result will give him the weight of the gumballs alone.
It's important to note that the weight of the gumballs may vary depending on their size, density, and the material of the bag. Different types of gumballs may have different weights. To get an accurate measurement, Nicholas should use a precise weighing instrument and account for any external factors that could affect the weight, such as moisture or contaminants.
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The price of everything in the store is reduced by 1/4 each hour until closing time. Liz wants to purchase a shirt that was originally marked at 24$. You can use a function to describe the shirts price x hours after the sale starts.
what is the answer to this problem 2 ft 5 in + 9 in =
The problem requires adding two measurements in different units, 2 ft 5 in and 9 in. We need to determine the sum of these measurements.
To add the given measurements, we should first convert them to a consistent unit. In this case, we will convert everything to inches since the second measurement is already in inches.
1 foot is equal to 12 inches, so 2 ft is equal to 2 * 12 = 24 inches. Therefore, 2 ft 5 in can be written as 24 in + 5 in. Adding 24 in and 5 in, we get 29 in. Thus, the sum of 2 ft 5 in and 9 in is 29 inches. In conclusion, when we add 2 ft 5 in and 9 in, the result is 29 inches.
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The total salamander population on the island is represented by the expression 3,000 (1.035) t, where t is the time in years. what is the equivalent exponential expression rewritten to identify the weekly growth rate of the population?
A.) 3000(1.035⁵²)t
B.) 3000(1.035) t/⁵²
C.) 3000(1.035 ¹/⁵²)t
D.) 3000(1.035 ¹/⁵²)⁵²t
Answer:
The correct answer is:
C.) 3000(1.035^(1/52))^t
This expression represents the equivalent exponential expression that identifies the weekly growth rate of the population. The exponent 1/52 represents the conversion from years to weeks, as there are 52 weeks in a year.
Step-by-step explanation:
One link in a chain was made from a cylinder that has a radius of 2. 5 cm and a height of 22 cm. How much plastic coating would be needed to coat the surface of the chain link? Use
3 14 for TT
O2512 cm
O 314 cm?
O 345 4 cm
O 471 cm
The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.
A cylinder's surface area is the overall area or region that the shape's surface covers. A cylinder's total surface area comprises both the area of the curved surface and the area of the two flat surfaces since there are two flat surfaces and one curved surface.
The formula for a particular cylinder's total surface area is as follows:
TSA = 2πr (h + r)
Given that;
One link in a chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm.
Hence, The plastic coating would be needed to coat the surface of the chain is,
2 × 3.14 × 2.5 × 22
= 345.4 cm²
So, The plastic coating would be needed to coat the surface of the chain is 345.4 cm². Hence option 3 is true.
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Let f(x)=−32x and g(x)=(12)x−1. Graph the functions on the same coordinate plane. What are the solutions to the equation f(x)=g(x) ? Enter your answers in the boxes. X = or x =.
The solutions to the equation f(x) = g(x) are x = 1/65. Hence, this is our final answer.
We have the following functions to graph:f(x)=−32x and g(x)=(12)x−1.Similarly, to graph the above functions we would require a table of values. For this we set x = −2, −1, 0, 1, 2 and solve for f(x) and g(x):x -2 -1 0 1 2f(x) 192 96 0 −32 −64g(x) 0.25 0.5 1 2 4Once we get the table of values, we can then graph the functions on the same coordinate plane.
We have the graph as below:Graph of f(x) = −32x and g(x) = (1/2)x−1Now to get the solutions to the equation f(x) = g(x), we equate the two expressions:−32x = (1/2)x−1Multiplying both sides by 2, we get:-64x = x - 1Collecting like terms, we get:-65x = -1Dividing both sides by -65, we get:x = 1/65
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Reflect the triangle across the y-axis, and then translate the image 5 units down. The final image is the same as which of the following transformations? Translate 5 units down, and then reflect over the x-axis. Translate 5 units down, and then reflect over the y-axis. Rotate 180° about the origin. Reflect over the x-axis, and then translate 5 units left.
The final image obtained after reflecting the triangle across the y-axis and translating it 5 units down is equivalent to reflecting the original triangle over the x-axis and then translating it 5 units down.
When we reflect the triangle across the y-axis, each point's x-coordinate is negated while the y-coordinate remains unchanged. This reflection essentially flips the triangle horizontally.
After reflecting the triangle, we then translate it 5 units down. This translation involves shifting each point of the triangle downward by 5 units along the y-axis.
Now let's consider the second transformation: reflecting the original triangle over the x-axis and then translating it 5 units down.
Reflecting the triangle over the x-axis means that each point's y-coordinate is negated while the x-coordinate remains unchanged. This reflection flips the triangle vertically.
After reflecting the triangle, we translate it 5 units down, which involves shifting each point of the triangle downward by 5 units along the y-axis.
By comparing the two sequences of transformations, we can see that they result in the same final image. First, we horizontally flip the triangle and then shift it downward, which is equivalent to first vertically flipping the triangle and then shifting it downward.
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Answer:
B. Translate 5 units down, and then reflect over the y-axis.
Step-by-step explanation:
Write log12 in four different ways. Name each you use and explain your process
The logarithm base 12 can be expressed as log12 or in exponential form as 12^x = y, where x is the exponent and y is the result.
The logarithm function is the inverse of exponentiation. It represents the exponent to which a given base (in this case, 12) must be raised to obtain a certain value. There are four different ways to express log12:
Logarithmic form: log12(y) - This notation indicates that the logarithm base 12 is being applied to a value y.
Exponential form: 12^x = y - In this form, the base 12 is raised to an exponent x to produce a value y.
Fractional exponent form: y^(1/12) - The fractional exponent represents the root of y with a base of 12. It is equivalent to log12(y).
Common logarithm form: log(y) / log(12) - If the logarithm base 12 function is not directly available, we can use the common logarithm (base 10) or any other logarithmic base and apply the change of base formula. The result is the logarithm of y divided by the logarithm of 12.
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Steve determines that sides DK and BC are congruent. He also measures
Therefore, the measure of the angle BDK is 62.5°.
Given: Steve determines that sides DK and BC are congruent. Therefore, DK ≅ BC.
He also measures the angle DBK to be 55°. Therefore, ∠DBK = 55°.
To find the measure of the angle BDK, we can use the fact that the sum of the angles in a triangle is 180°.
∠BDK = 180° - ∠DBK - ∠BKD
Since DK ≅ BC, ∠BDK = ∠BCD.
∴ ∠BDK = ∠BCD = (125° - ∠BCD)
Simplifying the equation, we get:
2∠BCD = 125°
∠BCD = 62.5°
Therefore, the measure of the angle BDK is 62.5°.
Hence, option D is correct.
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The starting numbers for the patterns for x and y are shown in the table below.
The blanks in the table represent the next four terms for each of the patterns.
• The rule for the x-values is add 3.
•The rule for the y-values is add 6.
X
y
0
0
Which graph represents the ordered pairs of the first five terms of the patterns
from the table?
The graph that represents the ordered pairs of the first five terms of the patterns from the table is the line graph.
The graph that represents the ordered pairs of the first five terms of the patterns from the table is the **line graph**.
The x-values in the table are increasing by 3 each time, while the y-values are increasing by 6 each time. This means that the ordered pairs are forming a straight line. The line graph is the only graph that shows a straight line.
The other graphs are either curves or not straight lines. The **scatter plot** shows a cloud of points that are not evenly distributed. The **bar graph** shows a series of vertical bars that are not evenly spaced. The **histogram** shows a series of horizontal bars that are not evenly spaced.
Here is a table of the first five terms of the patterns from the table, along with the corresponding ordered pairs:
X | Y | Ordered Pair
-- | -- | --
0 | 0 | (0, 0)
3 | 6 | (3, 6)
6 | 12 | (6, 12)
9 | 18 | (9, 18)
12 | 24 | (12, 24)
As you can see, the ordered pairs form a straight line.
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Jonas is conducting an experiment using a 10-sided die. He determines that the theoretical probability of rolling a 3 is StartFraction 1 over 10 EndFraction. He rolls the die 20 times. Four of those rolls result in a 3. Which adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer?.
To make the theoretical and experimental probabilities closer, Jonas can increase the sample size by conducting more rolls of the 10-sided die. This will provide a more accurate representation of the theoretical probability.
By increasing the sample size, Jonas can gather more data points, which can help to reduce the impact of random variations and provide a more accurate representation of the theoretical probability. As the number of rolls increases, the experimental probability is more likely to approach the theoretical probability.
In this case, Jonas can conduct more rolls of the 10-sided die beyond the initial 20 rolls. The larger the number of rolls, the better the experimental probability will reflect the theoretical probability of rolling a 3. By increasing the sample size, Jonas can minimize the impact of outliers or chance occurrences that may have influenced the results in the initial 20 rolls, resulting in a closer alignment between the theoretical and experimental probabilities.
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Complete steps 2 and 3 to solve the system of equations.
y = 4x – 5,
The solution of the given system of equations is (2, -10).
The given system of equations is:
y = 4x - 5
We need to solve the system of equations given by
Step 1: We need to substitute
y = 4x - 5 into the second equation.
4x - y = 5 becomes
4x - (4x - 5) = 5
Simplifying the above equation will give us:-
y + 4x - 4x = 5 + 5y = -10
Hence, the solution of the given system of equations is
(x, y) = (2, -10).
Steps 2 and 3 to solve the system of equations are:
Step 2: Substitute
y = 4x - 5 into the second equation. This gives us:
4x - (4x - 5) = 5
Simplifying the above equation will give us:-
y + 4x - 4x = 5 + 5
Step 3: Solve the simplified equation to get the value of y.-
y = 10y = -10
Thus, the solution of the given system of equations is (2, -10).
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30% of the members of a tennis club are pensioners. 36 members are pensioners
a) how many members there in total ?
b) how many members are not pensioners
Answer
there's 120 members in total
84 not pensioners
Explaination
36÷30% = 120
70% are not pensioners
so 70% × 120 = 84
or you could minus the pensioners from the total 120-36=84
Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related. The cost of each minute is constant.
A. What is the cost, c, ofa call of m minutes duration?
B. How long can you talk on the phone if you have $12 to spend?
The cost of a call of m minutes duration, given the cost of the calls would be c = 0. 05 + 0. 99m
If you have $ 12 to spend, the time you can spend is 10.15 minutes.
How to find the cost per minute ?The cost per minute would be :
= Difference between 5 and 10 minute call / Number of minutes
= ( 10. 86 - 5. 91 ) / 5
= $ 0.99
The cost per minute is therefore:
= 0. 99 x number of minutes
= 0. 99m
The initial cost is :
= 5 - 0. 99 x 5
= $ 0. 05
The number of minutes with $12 is:
= ( 12 - 0.05 ) / 0. 99
= 12. 1 minutes
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Nadia has £5 to buy pencils and rulers. She says,
"I will buy 15 pencils. Then I will buy as many rulers as possible
With my change I will buy more pencils. "
How many pencils and how many rulers does she buy?
Nadia has £5 to buy pencils and rulers. She says,"I will buy 15 pencils. Then I will buy as many rulers as possible. With my change, I will buy more pencils.
"Let the price of each pencil be p and the price of each ruler be r. Presenting the above scenario into the equation,15p + (x × r) = 5Here, x is the number of rulers to be bought. To minimize the number of pencils Nadia will buy with the change, we have to calculate the maximum number of rulers she can buy with the given £5.Let's assume Nadia buys a maximum of y rulers with all of her money, thus the number of pencils she will be left to buy will be,15p + (y × r) ≤ 5Therefore, Nadia can purchase 15 pencils and 2 rulers with £5 as shown below,15p + (2 × r) = 5Nadia can then buy more pencils with the remaining money, which is,£5 − [(15 × p) + (2 × r)] = Remaining money£5 − [(15 × 0.20) + (2 × 0.35)] = 0.40Hence, Nadia can buy 2 rulers and 15 pencils. She can buy only 2 rulers as many rulers she can buy with £5 is only 2.
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If a bike wheel covers a total of 69. 08 inches
after one complete rotation,what is the approximate radius of the bike wheel?
The approximate radius of the bike wheel is 11.0 inches.
If a bike wheel covers a total of 69.08 inches after one complete rotation, we can use the formula for the circumference of a circle to find the approximate radius of the bike wheel.
Circumference = 2piradius
where pi is approximately 3.14.
We are given that the circumference is 69.08 inches, so we can plug in these values and solve for the radius:
69.08 = 23.14radius
Dividing both sides by 2*pi, we get:
radius = 69.08 / (2*3.14) ≈ 11.0 inches
Therefore, the approximate radius of the bike wheel is 11.0 inches.
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Given the general form for linear systems: a1x b1y = c1 a2x b2y = c2 What is the correct solution using determinants, in terms of a, b and c?.
The solution to the linear system of equations in terms of a, b, and c is given by the values of x and y obtained from the determinants.
To solve the linear system of equations using determinants, we can use Cramer's Rule, which relies on the concept of determinants. The determinants involved in Cramer's Rule are the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy).
The general form of the linear system of equations is:
a1x + b1y = c1
a2x + b2y = c2
To find the solution using determinants, we first calculate the coefficient determinant (D):
D = | a1 b1 |
| a2 b2 |
The coefficient determinant D represents the determinant of the matrix formed by the coefficients of x and y.
Next, we calculate the x-determinant (Dx):
Dx = | c1 b1 |
| c2 b2 |
The x-determinant Dx is obtained by replacing the x-coefficients in the coefficient determinant D with the constants c1 and c2.
Similarly, we calculate the y-determinant (Dy):
Dy = | a1 c1 |
| a2 c2 |
The y-determinant Dy is obtained by replacing the y-coefficients in the coefficient determinant D with the constants c1 and c2.
Now, we can find the values of x and y using the determinants:
x = Dx / D
y = Dy / D
It's important to note that this method using determinants applies specifically to linear systems with two variables. For larger systems, the method becomes more complex and involves calculating determinants for higher-order matrices.
In summary, to find the solution using determinants, we calculate the coefficient determinant (D), the x-determinant (Dx), and the y-determinant (Dy) based on the given linear system of equations. Then, we find the values of x and y using the determinants. The solution is expressed in terms of a, b, and c.
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