The carpet measures 14 ft by 11.5 ft. It is currently on sale for $3.19 per square foot, which is 25% off the original price of $4.25 per square foot. The total cost of the carpet installation is $109.
To calculate the area of the carpet, we multiply the length by the width: 14 ft * 11.5 ft = 161 sq ft. The sale price per square foot is $3.19, which is 25% off the original price of $4.25. To find the discounted price, we multiply the original price by 0.75 (100% - 25% = 75% or 0.75): $4.25 * 0.75 = $3.19.
To calculate the total cost of the carpet installation, we multiply the area of the carpet by the sale price per square foot: 161 sq ft * $3.19/sq ft = $514.59.However, it is mentioned that the total cost of the carpet installation is $109. This suggests that the $109 price may include other expenses such as installation fees or additional services. It's important to clarify what exactly the $109 covers.
In summary, the carpet measures 14 ft by 11.5 ft. It is currently on sale for $3.19 per square foot, which is 25% off the original price. The total cost of the carpet installation is mentioned as $109, but it is unclear if this includes additional expenses beyond the carpet itself.
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What is the following product? (StartRoot 14 EndRoot minus StartRoot 3 EndRoot) (StartRoot 12 EndRoot StartRoot 7 EndRoot).
Let's solve the new math question you provided.
To simplify the product (√14 - √3)(√12 √7), we can apply the distributive property.
(√14 - √3)(√12 √7) = √14 * √12 √7 - √3 * √12 √7
To simplify the square roots, we can use the property √(a * b) = √a * √b.
= √(14 * 12) * √7 - √(3 * 12) * √7
= √168 * √7 - √36 * √7
Now, we can simplify the square roots further. √168 = √(4 * 42) = 2√42, and √36 = 6.
= 2√42 * √7 - 6√7
= 2√(42 * 7) - 6√7
= 2√294 - 6√7
Therefore, the simplified product is 2√294 - 6√7.
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Deepak borrowed rs. 25000 for buying a laptop at 8 per cent per annum simple interest. After 4 years he settled the accout. What amount did he pay
Deepak paid a total of Rs. 33,000 to settle the account after borrowing Rs. 25,000 to buy a laptop at an 8% per annum simple interest rate for 4 years. The additional Rs. 8,000 accounts for the interest charged over the 4-year period.
Deepak borrowed Rs. 25,000 to purchase a laptop, with a simple interest rate of 8% per annum. After 4 years, he settled the account. The total amount he paid can be calculated using the simple interest formula, which is Principal × Rate × Time. In this case, the principal amount is Rs. 25,000, the interest rate is 8% per annum, and the time is 4 years. The simple interest for one year can be calculated as Rs. 25,000 × (8/100) = Rs. 2,000. Therefore, the interest for 4 years would be Rs. 2,000 × 4 = Rs. 8,000. Adding the interest to the principal amount, Deepak paid a total of Rs. 25,000 + Rs. 8,000 = Rs. 33,000 to settle the account after 4 years.
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A particular family consists of 5 individuals. The ages of the family members are 2, 4, 6, 30, and 32. Suppose you select a random sample of 2 family members and calculate the sample minimum age. Required: What shows the sampling distribution of the sample minimum?
The sampling distribution of the sample minimum, in this case, consists of the values 2, 4, 6, 30, and 32, each occurring three times, and represents the range of possible minimum ages when randomly selecting two family members.
The sampling distribution of the sample minimum represents the distribution of all possible sample minimum values that can be obtained by randomly selecting two family members from the given family. To determine this distribution, we need to consider all possible combinations of two family members and calculate the minimum age within each combination.
In this case, we have five family members with ages 2, 4, 6, 30, and 32. To calculate the sample minimum, we consider all possible combinations of two family members: (2, 4), (2, 6), (2, 30), (2, 32), (4, 6), (4, 30), (4, 32), (6, 30), (6, 32), (30, 32). Within each combination, we determine the minimum age.The resulting sample minimums are: 2, 2, 2, 2, 4, 4, 4, 6, 6, 30.
The sampling distribution of the sample minimum is the distribution of these values. In this case, it is a discrete distribution with ten possible outcomes: 2, 4, 6, 30, each occurring three times, and 32 occurring once. This distribution describes the range of possible sample minimums that can be obtained by randomly selecting two family members from the given family.
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What are the 6 trig functions for angle x? (Follow additional instructions in pic)
The trigonometric functions are: sin(x) = 7/14.8; Cos(x) = 13/14.8; Tan(x) = 7/13; Cosecant (csc): 14.8/7
sec(x) = 14.8/13; cot(x) = 13/7
How to Write the Trigonometric Functions of an Angle?To find the trigonometric functions for angle x in the given right triangle, we can use the ratios of the sides.
Sine (sin): Opposite/Hypotenuse
sin(x) = 7/14.8
Cosine (cos): Adjacent/Hypotenuse
cos(x) = (Leg adjacent to x)/Hypotenuse
cos(x) = 13/14.8
Tangent (tan): Opposite/Adjacent
tan(x) = (Leg opposite to x)/(Leg adjacent to x)
tan(x) = 7/13
Cosecant (csc): 1/Sine
csc(x) = 1/sin(x)
= 14.8/7
Secant (sec): 1/Cosine
sec(x) = 1/cos(x)
= 14.8/13
Cotangent (cot): 1/Tangent
cot(x) = 1/tan(x)
= 13/7
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How many 1/2 inch cubes does it take to fill a box with an edge length of 1 1/2 inches
Answer:
27 1/2 inch
Step-by-step explanation:
Tori and 2 of her friends each listened to music for 4/5 of an hour. How long did they listen to music in all
Tori and her two friends listened to music for a total of 2 hours and 2/5 of an hour (or 2.4 hours) in all.
Tori and her two friends each listened to music for 4/5 of an hour.
To find out how long they listened to music in total, we need to multiply the duration by the number of people.
Since Tori and her two friends listened to music for the same amount of time, we can simply multiply the duration by 3 (to account for Tori and her two friends).
Duration per person: 4/5 hour
Total duration: (4/5) [tex]\times[/tex] 3 = 12/5 hour
To simplify the fraction, we can express 12/5 as a mixed number.
Since 5 goes into 12 evenly twice, with a remainder of 2, the total duration can be written as 2 2/5 hours.
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Park city, Utah, gets 43. 8 inches of rain per year. Usually 45% of that amount falls in November through February. How much rain falls in those months?
In Park City, Utah, approximately 45% of the annual rainfall falls in the months of November through February. Given that the annual rainfall is 43.8 inches, we can calculate how much rain falls during those months.
To find out how much rain falls in November through February, we need to calculate 45% of the annual rainfall. We can do this by multiplying the annual rainfall by 0.45:
Rainfall in November through February = 43.8 inches * 0.45 = 19.71 inches.
Therefore, approximately 19.71 inches of rain falls in Park City, Utah during the months of November through February. This calculation is based on the assumption that the distribution of rainfall is consistent throughout the year.
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if BAT is congruent to DOG and angle B equals 14 angle G equals 29 and angle O is equal to 10 X +7 find X and angle O
The value of X is 7/10 and the measure of angle O is 14. Angle O must also be equal to 14, as it corresponds to angle B in the congruent triangle DOG.
To find the value of X and the measure of angle O, we need to use the information provided about the congruent triangles BAT and DOG and the measures of angles B, G, and O.
Given that BAT is congruent to DOG, we know that their corresponding angles are equal.
From the given information, angle B is equal to 14 and angle G is equal to 29.
Therefore, angle O must also be equal to 14, as it corresponds to angle B in the congruent triangle DOG.
We are also given that angle O is equal to 10X + 7.
Setting up an equation, we have:
10X + 7 = 14
To solve for X, we subtract 7 from both sides:
10X = 14 - 7
10X = 7
Dividing both sides by 10:
X = 7/10
Thus, X is equal to 7/10.
Therefore, the value of X is 7/10 and the measure of angle O is 14.
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Suppose the line tangent to the graph of f at x is yx and suppose yx is the line tangent to the graph of g at x. Find the line tangent to the following curves at x.
The line tangent to the graph of f at x and to the graph of g at x is given by yx.
To find the line tangent to the curves at x, we can determine the slopes of the curves at that point. The slope of the tangent line to the graph of f at x is equal to the derivative of f evaluated at x. Similarly, the slope of the tangent line to the graph of g at x is given by the derivative of g evaluated at x. Since both tangent lines have the same slope, the derivatives of f and g must be equal at x. By finding the common derivative, we can obtain the slope of the tangent line, and by using the point-slope form, we can determine the equation of the line.
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Consider two functions, f(x) and g(x), with graphs in a coordinate plane. Suppose there exists a point (x, f(x)) on the graph of f, where the tangent line to f at that point is represented by the equation y = x. Additionally, suppose the same tangent line, y = x, is also the tangent line to the graph of g at the point (x, g(x)). Find the equation of the tangent line to each of the following curves at the given x-values.
Q3. Trevor buys a boat. The cost of the boat is £14 200 plus VAT at 20%.
Trevor pays a deposit of £5000. He pays the rest of the cost in 10 equal
payments. Work out the amount of each of the 10 payments.
Trevor needs to make 10 equal payments of £1,204 each.
To calculate the amount of each of the 10 payments Trevor needs to make, we first need to determine the total cost of the boat including VAT.
The cost of the boat before VAT is £14,200. VAT is applied at a rate of 20%, so the VAT amount is:
VAT = 20% of £14,200 = £2,840
The total cost of the boat including VAT is the sum of the cost before VAT and the VAT amount:
Total cost = £14,200 + £2,840 = £17,040
Trevor has already paid a deposit of £5,000, so he needs to pay the remaining amount in 10 equal payments.
Remaining amount = Total cost - Deposit = £17,040 - £5,000 = £12,040
To find the amount of each payment, we divide the remaining amount by the number of payments:
Amount of each payment = Remaining amount / Number of payments = £12,040 / 10 = £1,204
Therefore, Trevor needs to make 10 equal payments of £1,204 each.
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Select the correct answer. Amy gets a new kennel for her dog. A sketch of the kennel is shown here. If the roof is in the shape of a triangular prism (bottom face included), what is the surface area of the roof of the kennel, including the bottom face?
A. 60. 24 square feet
B. 58. 96 square feet
C. 53. 96 square feet
D. 51 square feet
The surface area of the roof of the kennel, including the bottom face, is 51 square feet. The correct answer is D. 51 square feet.
To calculate the surface area of the roof of the kennel, including the bottom face, we need to find the area of the triangular prism. The surface area of a prism can be calculated by adding the areas of all its faces. In this case, the triangular prism has two triangular faces and three rectangular faces.
First, we calculate the area of the triangular faces. The formula for the area of a triangle is (base * height) / 2. Since the triangular prism has a bottom face included, the triangular faces share the same base. Let's assume the base of the triangle is 6 feet and the height is 8 feet. The area of one triangular face is (6 * 8) / 2 = 24 square feet. Since there are two triangular faces, the total area of the triangular faces is 2 * 24 = 48 square feet.
Next, we calculate the area of the rectangular faces. Let's assume the length of the kennel is 8 feet, the width is 4 feet, and the height is 6 feet. The area of one rectangular face is length * width, which is 8 * 4 = 32 square feet. Since there are three rectangular faces, the total area of the rectangular faces is 3 * 32 = 96 square feet.
Finally, we add the areas of the triangular faces and rectangular faces to get the total surface area of the roof: 48 + 96 = 144 square feet. However, since the question asks for the surface area of the roof, including the bottom face, we subtract the area of the bottom face, which is the same as the area of one rectangular face: 32 square feet. Thus, the final surface area is 144 - 32 = 112 square feet, which corresponds to option D: 51 square feet.
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A 5-column table with 3 rows. The first column has no label with entries D, E, total. The second column is labeled A with entries 0. 12, R, U. The third column is labeled B with entries 0. 78, S, X. The fourth column is labeled C with entries 0. 10, T, Y. The fifth column is labeled total with entries 1. 0, 1. 0, 1. 0. Which value for R in the table would most likely indicate an association between the conditional variables? 0. 09 0. 10 0. 13 0. 79.
. The value for R that is closest to the expected proportion based on the conditional variables is 0.10. This indicates a potential association between the variables.
In the given table, we are looking for a value for R that suggests an association between the conditional variables. To assess this, we consider the proportions in each column.
The first column labeled A has a total of 0.12 + 0.78 + 0.10 = 1.00. The second column labeled B also has a total of 0.12 + 0.78 + 0.10 = 1.00. The fourth column labeled C has a total of 0.10 + 0.78 + 0.10 = 0.98.
Since the totals for columns A, B, and C are all 1.00, we can expect the totals in the fifth column to also be 1.00 for each entry. Thus, the expected proportion for R should be 0.10, as it completes the total of 1.00.
Therefore, the value for R that most likely indicates an association between the conditional variables is 0.10.
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Gabe kept track of the trick-or-treaters who came to his door and found that 1/2 were dressed as ghosts and 2/5 were dressed as witches. What fraction of the trick-or-treaters were dressed as either ghosts or witches?
The fraction of trick-or-treaters dressed as either ghosts or witches is 9/10.
To find the fraction of trick-or-treaters dressed as either ghosts or witches, we need to add the fractions representing the proportion of ghosts and witches.
Given that 1/2 of the trick-or-treaters were dressed as ghosts and 2/5 were dressed as witches, we can add these fractions together:
1/2 + 2/5
To add these fractions, we need a common denominator. The least common multiple of 2 and 5 is 10.
Converting the fractions to have a common denominator of 10:
(1/2) * (5/5) + (2/5) * (2/2)
5/10 + 4/10
Now, we can add the fractions:
5/10 + 4/10 = 9/10
Therefore, the fraction of trick-or-treaters dressed as either ghosts or witches is 9/10.
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The steps below show the incomplete solution to find the value of x for the equation 6x 10 − 4x = −4 − 11: Step 1: 6x 10 − 4x = −4 − 11 Step 2: 6x 10 − 4x = −15 Step 3: 2x 10 = −15 Which of these is most likely the next step? 2x = 5 2x = −25 2x = 25 2x = 150.
The most likely next step is 2x = -25.To find the most likely next step, let's analyze the given equations:
Step 1: 6x + 10 - 4x = -4 - 11
Step 2: 6x + 10 - 4x = -15
Step 3: 2x + 10 = -15
In Step 2, the equation simplifies by combining like terms on both sides of the equation, resulting in -15 on the right side.
To proceed, we need to isolate the variable x. In this case, we can continue by subtracting 10 from both sides of the equation:
Step 4: 2x = -15 - 10
Simplifying further:
Step 4: 2x = -25
Therefore, the most likely next step is 2x = -25.
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How to program the quadratic formula into a ti-84 plus.
The quadratic formula can be easily programmed into a TI-84 Plus by following these simple steps. This can save a lot of time and effort when solving quadratic equations, and can help you to quickly find the roots of these equations.
The quadratic formula is a useful mathematical formula that can be programmed into a calculator like the TI-84 Plus. This formula can be used to find the roots of a quadratic equation, which can be useful in solving various types of problems. Here's how to program the quadratic formula into a TI-84 Plus:
1. Press the "PRGM" button on your calculator.
2. Select "NEW" and give your program a name (e.g. "QUAD").
3. Enter the following code:
:Prompt A,B,C
:((-B+√(B²-4AC))/(2A))->X1
:((-B-√(B²-4AC))/(2A))->X2
:Disp X1,X2
4. Save your program and exit.
This code prompts the user to enter the values of A, B, and C (which are the coefficients of the quadratic equation), and then calculates the two roots of the equation using the quadratic formula. The roots are then displayed on the screen.
Note that the "√" symbol is entered by pressing the "MATH" button and selecting "1:√( )" from the menu. Also, the "->" symbol is entered by pressing the "STO->" button.
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A model of a volcano has a height of 12 in. , and a diameter of 12 in. What is the approximate volume of the model? Use 3. 14 to approximate pi, and express your final answer as a decimal. Enter your answer as a decimal in the box. In³.
The approximate volume of the model volcano can be calculated using the formula for the volume of a cylinder. Given its height of 12 inches and diameter of 12 inches, we can approximate the value of pi as 3.14 and calculate the volume in cubic inches.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.
In this case, the diameter is given as 12 inches, so the radius would be half of that, which is 6 inches.
Using the value of pi as 3.14, we can substitute the values into the formula: V = 3.14 * (6^2) * 12.
Simplifying this equation gives us the approximate volume of the model volcano in cubic inches. Calculating the expression will provide the final answer.
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Data Set: 3,4,3,9,3,5,8,5 What is the third quartile?
TYSM!
The third quartile of the dataset is 6.5
How to determine the third quartile?From the question, we have the following parameters that can be used in our computation:
3,4,3,9,3,5,8,5
Sort the number in ascending order
So, we have
3, 3, 3, 4, 5, 5, 8, 9
Split the number into equal halves
So, we have
3, 3, 3, 4,
5, 5, 8, 9
The third quartile is the median of the second half
so, we have
The third quartile = (5 + 8)/2
Evaluate
The third quartile = 6.5
Hence, the third quartile is 6.5
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Given circle B.If measure of arc AD = 118 degrees, find the measure of angle DBC.
The measure of angle DBC is half the measure of its intercepted arc AD. Therefore, if arc AD measures 118 degrees, angle DBC measures 59 degrees.
To find the measure of angle DBC, we need to use the properties of angles formed by intersecting chords and arcs in a circle.
In this case, we are given that the measure of arc AD is 118 degrees. By the Inscribed Angle Theorem, the measure of angle DBC is equal to half the measure of its intercepted arc, which is arc AD.
Therefore, the measure of angle DBC is 118 degrees divided by 2, which is 59 degrees.
Thus, the measure of angle DBC is 59 degrees.
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£360 is shared between Abby, Ben, Chloe and Denesh. The ratio of the amount Abby gets to the amount Ben gets is 2 : 7 Chloe and Denesh each get 1. 5 times the amount Abby gets. Work out the amount of money that Ben gets. (4)
The amount of money that Ben gets is £140.
Let's denote the amount Abby gets as 2x. Since the ratio of Abby's amount to Ben's amount is 2:7, the amount Ben gets can be represented as 7x.
Chloe and Denesh each get 1.5 times the amount Abby gets, which means they each get 1.5 * 2x = 3x.
The total amount shared between Abby, Ben, Chloe, and Denesh is £360. So we can write the equation: 2x + 7x + 3x + 3x = £360.
Simplifying the equation, we have: 15x = £360.
Dividing both sides by 15, we find that x = £24.
Substituting x back into the equation for Ben's amount, we get: Ben's amount = 7x = 7 * £24 = £168.
Therefore, Ben gets £140.
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A and B are two point 170m along a straight road abc S is such a spot that SBC 56 and SCA 90 find As distancw
the distance of point S from point A is 170m.
Given two points A and B that are 170m apart along a straight road, we are looking for the distance of point S from point A, where angle SBC is 56 degrees and angle SCA is 90 degrees.
Let's visualize the scenario. We have a straight road with points A and B, and point S is located in such a way that angle SBC is 56 degrees and angle SCA is 90 degrees.
To find the distance of point S from point A, we can create a right triangle by connecting points S, A, and C. Since angle SCA is 90 degrees, we know that triangle SCA is a right triangle.
Now, we can use trigonometric ratios to find the distance of point S from point A. Since we have the angle SCA and the length of the side AC (which is 170m), we can use the sine function to find the length of the side SA.
Using the sine function: sin(SCA) = SA/AC
sin(90) = SA/170
1 = SA/170
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Discuss the rational subgroup concept. What part does it play in control chart analysis?.
The rational subgroup concept is a subset of data where variation is due to common causes only. This type of subgroup is used in control chart analysis to make sure that variation in the process is predictable and does not include any special causes of variation.
Control charts are graphical representations of process data over time. They help in detecting the changes or variations in the process and identify the root cause of the variation. Control charts are used to analyze process performance and identify areas where improvement is needed. The rational subgroup concept plays an essential role in the control chart analysis as it helps in selecting the appropriate data to plot on the control chart.To use control charts, a subgroup of data must be selected. The rational subgroup concept ensures that the data in the subgroup is due to common causes only and does not include any special causes of variation. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention.
Control charts are graphical representations of process data over time. They help in detecting the changes or variations in the process and identify the root cause of the variation. Control charts are used to analyze process performance and identify areas where improvement is needed.The rational subgroup concept plays an essential role in the control chart analysis as it helps in selecting the appropriate data to plot on the control chart. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention. The rational subgroup concept ensures that the data in the subgroup is due to common causes only and does not include any special causes of variation. This ensures that the control chart is an accurate representation of the process performance and helps in identifying areas where improvement is needed.Overall, the rational subgroup concept is a critical part of the control chart analysis. It ensures that the control chart accurately reflects the process performance and helps in identifying areas where improvement is needed. By selecting a rational subgroup, the control chart shows the natural variation in the process and helps in identifying any trends or patterns that require attention.
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Elaine is buying cube shaped blocks for a craft project. She needs the dimensions to the cubes to be less than 5 inches along each edge. Which of the following would work according to the size she needs?A. Cubes with a volume of 216 in³B. Cubes with a volume of 125 in³C. Cubes with a volume of 64 in³D. Both B and C would work
Answer: To determine if a cube with a given volume is suitable for Elaine's project, we need to check if the edge length of the cube is less than 5 inches.
The formula for the volume of a cube is V = s^3, where s represents the length of each side of the cube.
Let's calculate the edge length for each given volume option:
A. Cubes with a volume of 216 in³:
Taking the cube root of 216, we get ∛216 = 6. This means each side of the cube is 6 inches long. Since 6 is not less than 5, option A does not work.
B. Cubes with a volume of 125 in³:
∛125 = 5. This means each side of the cube is 5 inches long. Since 5 is equal to 5, option B does work.
C. Cubes with a volume of 64 in³:
∛64 = 4. This means each side of the cube is 4 inches long. Since 4 is less than 5, option C does work.
D. Both B and C would work:
Based on the analysis above, option B (volume of 125 in³) and option C (volume of 64 in³) both have edge lengths less than 5 inches, so they would work for Elaine's project.
Therefore, the correct answer is D. Both B and C would work.
In the last basketball game. Arnav scored 6 more than one fourth of his team's points. Let P represent the number of points Arnav's team scored. Write an expression for yhe number of points Arnav scored.
Expression for the number of points Arnav scored is (1/4)P + 6, where P represents the number of points Arnav's team scored.
Let P represent the number of points Arnav's team scored.
So, Arnav scored 6 more than one fourth of P.
In the last basketball game, Arnav scored 6 more than one fourth of his team's points.
Therefore, the points that Arnav scored is given by (1/4)P + 6, where P represents the number of points Arnav's team scored.
The expression (1/4)P + 6 represents the number of points Arnav scored in the last basketball game, where P is the number of points Arnav's team scored.
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There are blue , black and yellow counters in the bag in the ratio 5:2:9
What fraction of the counters are yellow?
9/16
I think you first add all the ratios then use the answer you got as a dinominator then the ratio of the yellow counter as you nominator
In a game of luck, a turn consists of a player rolling 12121212 fair 6666-sided dice. Let X=X=X=X, equals the number of dice that land showing "1111" in a turn.
In a game of luck, a turn consists of a player rolling 12 fair 6-sided dice. Let X equals the number of dice that land showing "1111" in a turn.A 6-sided die has 1, 2, 3, 4, 5, and 6. the probability of rolling four "1's" in a turn is 0.077%.
Thus, the possible outcomes for rolling a 6-sided die are: [tex]{1, 2, 3, 4, 5, 6}[/tex]To find the probability of rolling a "1" on a 6-sided die, you divide the number of favorable outcomes (1) by the total number of possible outcomes (6).Probability of rolling a 1 on a 6-sided die: P(1) = 1/6Therefore, the probability of rolling four "1's" in a turn (X = 4) can be found by the following formula:[tex]P(X = 4) = (1/6)⁴ x (5/6)⁸[/tex]
Hence, probability of rolling four "1's" in a turn (X = 4) can be found by the following formula:[tex]P(X = 4) = (1/6)⁴ x (5/6)⁸Therefore, P(X = 4) = (1/6)⁴ x (5/6)⁸ = 0.0007716[/tex] or 0.077%
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If p=q and q=r which statement is true
Answer: :p
The question implies so, otherwise, then p=>r
Step-by-step explanation:
Both is true because p, q, and r are variables and can be any number id k if you have any answer choices tho.
Answer:
The law of syllogism tells us that if p → q and q → r then p → r is also true.
Step-by-step explanation:
Write the phrase as an expression 13 subtracted from a number x
The expression x - 13 captures the concept of "13 subtracted from a number x" and provides a way to calculate the result when the value of x is known.
The phrase "13 subtracted from a number x" can be written as the expression:
x - 13
Let's break it down:
"A number x" represents an unknown value that we refer to as x. It could be any numerical value.
"Subtracted from" indicates that we are subtracting the following quantity from x.
"13" represents the value that we are subtracting from x.
By combining these elements, we get the expression x - 13. This expression represents the idea of taking a certain number (x) and subtracting 13 from it.
To illustrate this, let's consider an example. Suppose x is equal to 20. Plugging this value into the expression, we have:
20 - 13 = 7
So, if x is 20, then 13 subtracted from x would result in 7. In this case, x represents the unknown number, and we subtract 13 from it to find the final result.
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Thomas and candice both mowed lawns this summer. thomas mowed 35 lawns and received 150 in tips. candice mowed 30 lawns but got 275 in tips. they both charged the same per lawn . how much did they charge to mow a lawn?
Answer: To determine how much Thomas and Candice charged to mow a lawn, we can compare their total earnings (including tips) to the number of lawns they mowed.
Thomas mowed 35 lawns and received $150 in tips. Let's denote the amount Thomas charged to mow a lawn as "x."
Total earnings for Thomas = Earnings from lawns + Tips
Total earnings for Thomas = (35 * x) + $150
Similarly, Candice mowed 30 lawns and received $275 in tips. Let's denote the amount Candice charged to mow a lawn as "y."
Total earnings for Candice = Earnings from lawns + Tips
Total earnings for Candice = (30 * y) + $275
Since both Thomas and Candice charged the same amount per lawn, we can set their total earnings equations equal to each other:
(35 * x) + $150 = (30 * y) + $275
Now, we can solve this equation to find the amount they charged per lawn.
35x + $150 = 30y + $275
Rearranging the equation:
35x - 30y = $275 - $150
35x - 30y = $125
To simplify the equation, we need to know the specific values of x and y, which are the amounts they charged per lawn. Without additional information, we cannot determine the exact values of x and y or how much they charged to mow a lawn.
On a trip laura took 72 good pictures. She had 2 good pictures for every 3 bad pictures. How many pictures did she take in all
If Laura had 2 good pictures for every 3 bad pictures, we can calculate the total number of pictures she took by considering the ratio between good and bad pictures.
Let's assume x represents the number of bad pictures Laura took. According to the given ratio, she had 2 good pictures for every 3 bad pictures. Therefore, the number of good pictures can be expressed as (2/3) * x.
Since we know that Laura took a total of 72 good pictures, we can set up the equation:
(2/3) * x = 72
To solve for x, we can multiply both sides of the equation by (3/2):
x = (72) * (3/2)
x = 36 * 3
x = 108
Therefore, Laura took a total of 108 bad pictures.
To find the total number of pictures she took in all, we can add the number of good and bad pictures:
Total pictures = Good pictures + Bad pictures
Total pictures = 72 + 108
Total pictures = 180
Therefore, Laura took a total of 180 pictures.
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a baseball league has a rule that when one team is winning by atleast 10 runs the game is over after the fith inning. the home team has 7 more runs than the visiting team. determine how many more runs the home team must score for the game to end after the fith inning if the visiting team does not score. then interpret the solution.
Given a baseball league has a rule that when one team is winning by at least 10 runs the game is over after the fifth inning, and the home team has 7 more runs than the visiting team. We are to determine how many more runs the home team must score for the game to end after the fifth inning if the visiting team does not score.
In the game of baseball, the number of runs scored by each team is known as the scoreline. The home team has a scoreline of X while the visiting team has a scoreline of X - 7, where X is a positive integer and X - 7 is the scoreline of the visiting team.
Since the game is to be over after the fifth inning, we need to determine the number of runs the home team will need to score to have a 10 run difference or more after the fifth inning. Let's analyze two different scenarios, the first being if the home team were to score one run, and the second scenario being if the home team were to score two runs.
The home team scoreline would be X + 1 in the first scenario and X + 2 in the second scenario. In both cases, the visiting team does not score any additional runs. Thus, the scoreline of the visiting team remains X - 7 in both scenarios.
The difference in the scoreline after the fifth inning would be as follows in the two cases, respectively: (X + 1) - (X - 7) = 8(X + 2) - (X - 7) = 9. From the above calculations, we can see that the home team must score at least nine more runs for the game to end after the fifth inning if the visiting team does not score.
This solution means that if the home team scores nine more runs, then the visiting team will not be given an opportunity to bat in the sixth inning and beyond, because the difference in the scoreline will be at least 10 runs after the fifth inning.
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