Only the pair of ratios A (7/4, 21/12) forms a true proportion.
To determine which pair of ratios form a true proportion, we need to check if the ratios are equal.
Let's evaluate each pair of ratios:
A) 7/4 and 21/12:
To simplify both ratios:
7/4 = 1.75
21/12 = 1.75
Since both ratios are equal to 1.75, the pair of ratios A form a true proportion.
B) 6/3 and 5/6:
To simplify both ratios:
6/3 = 2
5/6 ≈ 0.83
The ratios 2 and 0.83 are not equal, so the pair of ratios B does not form a true proportion.
C) 7/10 and 6/7:
To simplify both ratios:
7/10 = 0.7
6/7 ≈ 0.86
The ratios 0.7 and 0.86 are not equal, so the pair of ratios C does not form a true proportion.
D) 3/5 and 7/12:
To simplify both ratios:
3/5 = 0.6
7/12 ≈ 0.58
The ratios 0.6 and 0.58 are not equal, so the pair of ratios D does not form a true proportion.
Therefore, only the pair of ratios A (7/4, 21/12) forms a true proportion.
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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:
Robert has a contrainer in the shape of a cube with an edge length of 6.1 cm
If Robert has a container in the shape of a cube with an edge length of 6.1 cm, we can calculate various properties of the cube.
Volume of the cube: The volume of a cube is calculated by cubing the length of its edges. In this case, the volume would be: Volume = (6.1 cm)^3 = 226.651 cm³ (rounded to three decimal places). Surface area of the cube: The surface area of a cube is calculated by multiplying the area of one face by the total number of faces (which is six for a cube). Since all the faces of a cube have the same area, we can find the area of one face and then multiply it by six. Surface Area = 6 * (6.1 cm)^2 = 223.092 cm² (rounded to three decimal places). Diagonal of the cube: The diagonal of a cube can be found using the Pythagorean theorem. In this case, Diagonal = √(6.1 cm)^2 + (6.1 cm)^2 + (6.1 cm)^2 = √(3 * (6.1 cm)^2) = √(3 * 37.21 cm²) ≈ 9.622 cm (rounded to three decimal places).
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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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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.
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:
The heights of mature maple trees are approximately normally distributed with a mean of 80 feet and a standard deviation of 12.5 feet. What proportion of mature maple trees are between 60 and 90 feet? (round to the nearest whole percent)
73% of mature maple trees are between 60 and 90 feet. The required percentage is 73%
Given that the heights of mature maple trees are approximately normally distributed with a mean of 80 feet and a standard deviation of 12.5 feet.
The formula for the z-score is given by:
z = (X - μ)/σ, where X = 60, μ = 80, and σ = 12.5
Substitute the values, we get
z = (60 - 80) / 12.5
= -1.6
The z-score for 60 feet is -1.6.
The formula for the z-score is given by:z = (X - μ)/σ, where X = 90, μ = 80, and σ = 12.5
Substitute the values, we get
z = (90 - 80) / 12.5= 0.8
The z-score for 90 feet is 0.8.
To find the proportion of mature maple trees between 60 and 90 feet, we need to find the area under the standard normal curve between z = -1.6 and z = 0.8.
Using the standard normal distribution table or calculator, we can find the area under the curve as follows:
Area = 0.7881 - 0.0516= 0.7365
Therefore, the proportion of mature maple trees between 60 and 90 feet is 73% (rounded to the nearest whole percent).
Hence, the correct answer is option (D).
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Jonathan purchased a new car in 2008 for $25,400. The value of the car has been
depreciating exponentially at a constant rate. If the value of the car was $7,500 in
the year 2015, then what would be the predicted value of the car in the year 2017, to
the nearest dollar?
HELP
well, first off let's find the rate its depreciating by, so hmm in 2008 it was $25,400 and then 7 years later it went down to $7,500, so
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 7500\\ P=\textit{initial amount}\dotfill &25400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &7\\ \end{cases} \\\\\\ 7500 = 25400(1 - \frac{r}{100})^{7} \implies \cfrac{7500}{25400}=\left( \cfrac{100-r}{100} \right)^7[/tex]
[tex]\cfrac{75}{254}=\left( \cfrac{100-r}{100} \right)^7\implies \sqrt[7]{\cfrac{75}{254}}=\cfrac{100-r}{100}\implies 100\sqrt[7]{\cfrac{75}{254}}=100-r \\\\\\ 100\sqrt[7]{\cfrac{75}{254}}-100=-r\implies 100-100\sqrt[7]{\cfrac{75}{254}}=r\implies \stackrel{ \% }{15.99}\approx r[/tex]
so hmmm how about in 2017? well, 2017 from 2008 would be 9 years later, so using that rate
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &25400\\ r=rate\to 15.99\%\to \frac{15.99}{100}\dotfill &0.1599\\ t=\textit{years}\dotfill &9\\ \end{cases} \\\\\\ A \approx 25400(1 - 0.1599)^{9} \implies A \approx 25400( 0.8401 )^{9}\implies \boxed{A \approx 5294}[/tex]
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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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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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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A fast-food restaurant sold 8,416 hamburgers in a week. if the restaurant opens 7 days a week, about how many hamburgers were sold each day?
Approximately 1,202 hamburgers were sold each day at the fast-food restaurant.
To determine how many hamburgers were sold each day, we can divide the total number of hamburgers sold in a week by the number of days the restaurant is open.
Given that the fast-food restaurant sold 8,416 hamburgers in a week and is open 7 days a week, we can calculate the approximate number of hamburgers sold each day.
8,416 hamburgers ÷ 7 days ≈ 1,202 hamburgers per day.
Therefore, approximately 1,202 hamburgers were sold each day at the fast-food restaurant.
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The distance covered by a boy in going 5 times around a square shaped park is 1025 m. What is the area of the park?
The area of the square-shaped park is approximately 2628.125 square meters.
Let's assume that the park is a perfect square, with each side equal to "x" meters.
If the boy covers a distance of 1025 m by going around the park 5 times, then the total distance covered by the boy is:
total distance = 5 * perimeter of the park
Since the park is a square, its perimeter is given by:
perimeter of park = 4 * x
So, we can write:
5 * 4 * x = 1025
Simplifying this equation, we get:
x = 1025 / 20 = 51.25
Therefore, each side of the square-shaped park is 51.25 meters long.
The area of the square is given by:
area of park = x^2
Substituting the value of "x", we get:
area of park = (51.25)^2 = 2628.125 sq.meters (approx)
Therefore, the area of the square-shaped park is approximately 2628.125 square meters.
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David charges $14 to shovel one driveway. He earned $112 in February. A) model this situation using an equation. B) Solve the equation to find out how many driveways David shovels in February
A) The situation can be modeled using the equation 14d = 112, where "d" represents the number of driveways David shoveled in February and 14 represents the amount charged per driveway.
B) Solving the equation, we find that David shoveled 8 driveways in February.
A) To model the situation, we can set up an equation based on the information given. Let's assume that David shoveled "d" driveways in February, and since he charges $14 per driveway, the total amount earned can be represented as 14d. Since he earned $112 in February, we can set up the equation: 14d = 112.
B) To find out how many driveways David shoveled in February, we solve the equation. Dividing both sides of the equation by 14, we get d = 112/14. Simplifying the right side gives us d = 8. Therefore, David shoveled 8 driveways in February.
In summary, the situation can be modeled using the equation 14d = 112, where "d" represents the number of driveways shoveled by David. By solving the equation, we find that David shoveled 8 driveways in February.
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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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What does the long-term failure of the religious reforms of Amenophis IV of Egypt tell us about the status of religion in Egyptian society?
The long-term failure of the religious reforms of Amenophis IV of Egypt tells us that religion in Egyptian society was deeply rooted in the worship of several deities so, it was impossible for Amenophis to replace these with just one god.
What the failure tells usAmenophis of Egypt was one of the Kings who sought to change the traditional system of worship in Egypt by telling the people to worship the sun god, Aten.
This move was rejected by the people who believed in many different gods. Akenaton also wanted to make himself the only priest and the priesthood rejected his move also.
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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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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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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
Janet cut 9 pieces of ribbon that were each 0.4 meter. She then cut 5 pieces of ribbon that were each 0.6 meter. How many meters of ribbon did Janet cut
Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.
Janet cut a total of 9 pieces of ribbon, each measuring 0.4 meters, and 5 pieces of ribbon, each measuring 0.6 meters.
To find the total length of ribbon Janet cut, we need to calculate the sum of the lengths of all the individual pieces.
For the 9 pieces of ribbon measuring 0.4 meters each, we can multiply the length of each piece by the number of pieces: 9 * 0.4 = 3.6 meters.
Similarly, for the 5 pieces of ribbon measuring 0.6 meters each, we can calculate the total length: 5 * 0.6 = 3 meters.
To find the total length of ribbon Janet cut, we add the lengths of the two sets of ribbons together: 3.6 + 3 = 6.6 meters.
Therefore, Janet cut a total of 6.6 meters of ribbon by combining the 9 pieces of 0.4-meter ribbon and the 5 pieces of 0.6-meter ribbon.
In summary, Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.
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A cylinder and a cone have the same height and the same base areas. If the volume of the cylinder is 66 cubic inches, what is the volume of the cone? (Use 3. 14 for Pi)
Answer:
The volume of the cone is 22 cubic inches.
Step-by-step explanation:
To find the volume of the cone, we need to use the formula for the volume of a cone:
Volume of a cone = (1/3) * π * r^2 * h
Given that the height and base area of the cylinder and cone are the same, we can assume that the radius of the cylinder's base is equal to the radius of the cone's base.
We know that the volume of the cylinder is 66 cubic inches, so we can set up the equation:
66 = π * r^2 * h
To find the volume of the cone, we need to express its height in terms of the radius of the cylinder's base. The height of the cone will be equal to the height of the cylinder.
Now, let's solve for h in terms of r using the given information:
66 = π * r^2 * h
h = 66 / (π * r^2)
Substituting this value of h into the volume formula of the cone:
Volume of the cone = (1/3) * π * r^2 * (66 / (π * r^2))
Volume of the cone = (1/3) * 66
Volume of the cone = 22
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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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solve the formula Q=cm(t2-t1) for t2, using two procedural steps. show all work
The formula given is Q=cm(t2-t1).
The problem requires that we solve this formula for t2. To achieve this, we will use two procedural steps. These steps are:
Step 1: Isolate (t2 - t1)
To isolate (t2 - t1), we begin by adding t1 to both sides of the equation.
This yields: Q + t1cm = (t2 - t1)cm
Step 2: Divide both sides by cm
To solve for t2, we need to remove the coefficient of (t2 - t1). This is achieved by dividing both sides by cm, which gives: t2 - t1 = Qcm + t1cm
Adding t1 to both sides, we have:
t2 = Qcm + t1
t2 = t1 + Qcm
Therefore, the formula for t2 is t2 = t1 + Qcm.
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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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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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In pitcher's era that earned run average ,A is measured by the formula A= 9R/I where R= runs allowed and I= number of inning's pitched solve the formula for I
To solve the formula A=9R/I for I, we need to rearrange the equation to isolate the variable I. By plugging in the values for A and R into the equation, we can determine the number of innings pitched.
Starting with the formula A=9R/I, we want to solve for I. To do this, we can begin by multiplying both sides of the equation by I to eliminate the fraction. This gives us AI = 9R.
Next, we want to isolate the variable I. To do so, we can divide both sides of the equation by A. This gives us AI/A = 9R/A, which simplifies to I = 9R/A.
Therefore, the solution to the formula A=9R/I for I is I = 9R/A. This equation allows us to calculate the number of innings pitched (I) when given the earned run average (A) and the runs allowed (R).By plugging in the values for A and R into the equation, we can determine the number of innings pitched.
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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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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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Juanita has 9 rings in her jewelry box. five are gold and 4 are silver. if she randomly selects 3 rings to wear to a party, find each probability.
the probability of Juanita randomly selecting 3 rings, where 2 are gold and 1 is silver, is 40/84, which simplifies to 5/21 or approximately 0.2381.
The probability of Juanita randomly selecting 3 rings, where 2 are gold and 1 is silver, can be calculated using combinations. The probability is 20/84 or approximately 0.2381.
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The number of ways to choose 2 gold rings out of 5 is given by the combination formula: C(5, 2) = 5! / (2! * (5-2)!) = 10.
The number of ways to choose 1 silver ring out of 4 is given by the combination formula: C(4, 1) = 4! / (1! * (4-1)!) = 4.
Since we want to choose 2 gold rings and 1 silver ring, we multiply these two combinations: 10 * 4 = 40.
The total number of ways to choose any 3 rings out of 9 is given by the combination formula: C(9, 3) = 9! / (3! * (9-3)!) = 84.
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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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Compare the investment below to an investment of the same principal at the same rate compounded
principal: $8,000, annual interest: 6%, interest periods: 4, number of years: 17
Investment 2, which is compounded annually, has a higher future value of $24,549.17 compared to Investment 1, which is compounded quarterly, with a future value of $23,048.52.
To compare the two investments, we need to calculate the future value of each investment and compare the results.
Investment 1:
Principal: $8,000
Annual interest rate: 6%
Interest periods: 4
Number of years: 17
Using the compound interest formula:
Future Value = Principal * (1 + (Annual interest rate / Interest periods))^(Interest periods * Number of years)
Future Value of Investment 1:
Future Value = $8,000 * (1 + (0.06 / 4))^(4 * 17)
Future Value = $8,000 * (1 + 0.015)^68
Future Value = $8,000 * (1.015)^68
Future Value = $23,048.52
Investment 2:
Principal: $8,000
Annual interest rate: 6%
Interest periods: 1
Number of years: 17
Future Value of Investment 2:
Future Value = $8,000 * (1 + 0.06)^17
Future Value = $8,000 * (1.06)^17
Future Value = $24,549.17
Therefore, investing the principal at the same rate but compounded annually would result in a higher return after 17 years.
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