Answers
The value of x to the nearest tenth are as follows;
x = 47.0 units.
x = 25.1 units.
x = 23.8 units.
x = 29.7 units.
x = 21.1°.
x = 39.6°.
x = 58.0°.
x = 72.9°.
How to determine the value of x?From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:
Opposite side = x.
Adjacent side = 25.
Therefore, we would determine the value of x by using Tan trigonometric function:
Tanθ = Opposite side/Adjacent side
Tan45 = 25/x
x = 25Tan62
x = 47.0 units.
For right-angled triangle 3, we have:
Sin26 = 11/x
x = 11/0.4384
x = 25.1 units.
For right-angled triangle 4, we have:
Sin48 = x/32
x = 32sin48
x = 23.8 units.
For right-angled triangle 5, we have:
Cos12 = 29/x
x = 29/0.9782
x = 29.7 units.
For right-angled triangle 6, we have:
Cosθ = 14/15
θ = cos⁻¹(0.9333)
θ = 21.1°.
For right-angled triangle 7, we have:
Tanθ = 19/23
θ = tan⁻¹(0.8261)
θ = 39.6°.
For right-angled triangle 8, we have:
Cosθ = 9/17
θ = cos⁻¹(0.5294)
θ = 58.0°.
For right-angled triangle 9, we have:
Sinθ = 43/45
θ = sin⁻¹(0.9556)
θ = 72.9°.
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Related Questions
What are the 7 metric units?
Answers
The 7 metric units are part of the International System of Units, and this are km, m, cm, mm, kg, g and L. Each unit is based on a multiple of 10, making it easy to convert between them. For example, 1 kilometer is equal to 1000 meters, and 1 kilogram is equal to 1000 grams.
What are the 7 metric units?The 7 metric units are as follows:
Kilometer (km) - used to measure distance.Meter (m) - used to measure length.Centimeter (cm) - used to measure small lengths.Millimeter (mm) - used to measure very small lengths.Kilogram (kg) - used to measure mass.Gram (g) - used to measure small amounts of mass.Liter (L) - used to measure volume.Learn more about the International System of Units here: https://brainly.com/question/14288881
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if a seed is planted, it has a 69% chance of growing into a healthy plant. let x be the number of seeds grow into healthy plants when 75 seeds are planted. what is the distribution of x? x ~ ? (,) please show the following answers to 4 decimal places. what is the probability that exactly 44 seeds grow into healthy plants? what is the probability that at least 44 seeds grow into healthy plants? what is the probability that more than 44 seeds grow into healthy plants? what is the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants?
Answers
The probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
The probability distribution of x, where x is the number of seeds that grow into healthy plants when 75 seeds are planted, is a binomial distribution with parameters n = 75 and p = 0.69. The probability of x = 44 is calculated by using the formula for the probability mass function of the binomial distribution:
[tex]P(x=44) = (75 choose 44) * (0.69)^44 * (1-0.69)^(75-44) = 0.1578[/tex]
The probability of x >= 44 is calculated by using the formula for the cumulative probability function of the binomial distribution:
[tex]P(x > = 44) = 1 - P(x < = 43) = 1 - (75 choose 43) * (0.69)^43 * (1-0.69)^(75-43) = 0.7406[/tex]
The probability of x > 44 is calculated by subtracting the probability of x = 44 from the probability of x >= 44:
P(x > 44) = P(x >= 44) - P(x = 44) = 0.7406 - 0.1578 = 0.5828
The probability of 19 <= x <= 53 is calculated by subtracting the probability of x <= 18 from the probability of x <= 53:
[tex]P(19 < =x < =53) = P(x < =53) - P(x < =18) = 0.9994 - 0.0053 = 0.9941[/tex]
Therefore, the probability that exactly 44 seeds grow into healthy plants is 0.1578, the probability that at least 44 seeds grow into healthy plants is 0.7406, the probability that more than 44 seeds grow into healthy plants is 0.5828, and the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
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Subtract and simplify. Show work to earn full credit. (9^2 − 4 − 4) − (−2^3 − + 12)
Answers
The simplified form of the numerical expression (9² - 4 - 4) - (- 2³ - + 12) is 93.
What is a numerical expression?Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.
Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
By mixing numbers with different mathematical operators, we can create a numerical expression. There is no restriction on how many operators can be used in a numerical expression. Between two numbers, some mathematical expressions utilize just one operator, whereas others may use multiple operators.
Given, An expression (9² - 4 - 4) - (- 2³ - + 12).
= (9×9 - 8) - (- 2×2×2 - 12).
= (81 - 8) - (- 8 - 12).
= (73) - (- 20).
= 73 + 20.
= 93.
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The diagram shows a prism
Draw the front elevation and the side elevation of the prism on the grids.
Use a scale of 2 squares to 1m
Answers
The sketch of the front elevation and the side elevation of the prism are added as an attachment
How to draw the front elevation and the side elevation of the prismFrom the question, we have the following parameters that can be used in our computation:
The prism
Using the figure as a guide, we understand that:
The front elevation is a rectangle of 2m by 0.5m
While the side elevation is a rectangle merged with a trapezoid
Next, we draw the elevations (see attachment)
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which three values are smaller than 1/2:
A. 1/4
B. 0.26
C. 3/5
D. 67%
E. 0.74
F. 40%
Answers
Answer: A, B, F
Step-by-step explanation:
For convenience sake, let's establish early on that 1/2 is equal to 0.5 or 50% in their decimal and percentage forms respectively.
- A as a decimal is 0.25, which is not only smaller than 1/2, but it is exactly half of the value, so A works.
- B is also smaller than the decimal of 0.5, therefore it counts.
- 3/5 as a decimal is 0.5, which is greater, so doesn't count.
- 67% is bigger than 50%, so doesn't count.
- 0.74 is bigger than 0.5, so doesn't count.
- 40% is smaller than 50%, so it counts.
Answer:
A, B, and F
Step-by-step explanation:
A. 1/4 = 25%
B. .26 = 26%
F. 40%
which trig function do you use cos, tan, sin and how it is solved
Answers
We can use the sine ratio to solve this problem and the value of x would be 8.604.
What are trigonometric ratios?
Trigonometric ratios are ratios of the side lengths of a right triangle with respect to its acute angles.
Sine (sin) ratio: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In the given figure, we have given the hypotenuse of the triangle, and an angle is given which is opposite to 35 degree, so we can use the sine ratio to find the value of x
sin35°= x/15
To solve for x, we can use the following steps:
Multiply both sides of the equation by 15 to isolate x:
sin 35° = x/15
15 * sin 35° = x
Use a calculator to approximate sin 35°:
sin 35° ≈ 0.5736
Substitute the approximation into the equation and solve for x:
x = 15 * 0.5736
x ≈ 8.604
Therefore, x is approximately equal to 8.604.
Hence, we can use the sine ratio to solve this problem and the value of x would be 8.604.
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find an obtuse angle, θ, such that 0 ≤ θ ≤ 2π and has the same sine as -275° (please explain)
Answers
The obtuse angle such that has the same sine as -275° is θ = 95°
How to find the angle θ?We want to find an obtuse angle (with a measure larger than 90°) in the range 0 ≤ θ ≤ 2π (or 0 < θ < 360°, after that we can change the units from degrees to radians) such that sin(θ) = sin(-275°)
First, remember that the sine function has a periodicity of 360°, then:
sin(-275°) = sin(-275° + 360°) = sin(85°)
Now we know that the sine function is symmetric around x = 90°
Then:
sin(90° + x) = sin(90° - x)
if we take x = 5° we will get:
sin(90° + 5°) = sin(90° - 5°)
sin(95°) = sin(85°) = sin(-275°)
Thus we can conclude that θ = 95°
That is the obtuse angle.
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Raito tables green blue
12 16
Blank 4
36 Blank
Answers
The ratio tables based on the information will be:
12 16
3 4
36 48
How to calculate the valuesRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.
Since the ratio is 3:4. When the smaller number is 36, the larger number will be:
= 4/3 × 36.
= 48
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Question 2 of 10
Frank is a champion fish charmer who can charm fish with .62 probability of
success. If he attempts to charm 100 fish, what's the probability he'll charm
between 60 and 80 inclusive? Solve using two methods: normal
approximation without the continuity correction, and normal approximation
with the continuity correction.
A. 332, 337
B. 323, .291
OC. 337,.332
OD. .660,.697
OE. 337,.323
Answers
The Solution using two methods are 323, .291, the correct option is B`.
How can we interpret probability?Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).
When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.
Given;
Frank is a champion fish charmer who can charm fish with .62 probability of success
He attempts to charm 100 fish, what's the probability he'll charm
between 60 and 80 inclusive
Now, probability out of 100
=62
This is between 60 and 80
So, 323
Therefore, the probability will be 323 and .291
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Select the correct answer. A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. Given: Transversal t passes through parallel lines r and s. Prove: ∠3 ≅ ∠6 ∠4 ≅ ∠5 Statement Reason 1. r || s given 2. ∠3 ≅ ∠7 ∠4 ≅ ∠8 For parallel lines cut by a transversal, corresponding angles are congruent. 3. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7 Reason: Congruent Supplements Theorem B. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180° Reason: Linear Pair Theorem C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Answers
Answer:
The correct answer is C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles.
This statement uses the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠3 and ∠6 are corresponding angles, and ∠4 and ∠5 are also corresponding angles, their measures must add up to 180 degrees in order for the parallel lines to be cut by the transversal.
Answer:
Option, D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Step-by-step explanation:
In this question that you have put:
7 ≅ ∠6 and ∠8 ≅ ∠5 Reason =
Vertical Angles Theorem ( Or in similar terms VAT )
Make sure that you remember the following:
vertical angles are the angles that are opposite each other when the two line " meet together "
Thus, your answer to your questions is.
D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
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what is the solution to 2j=16+4j
Answers
Answer: j = -8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
2j = 16 + 4j
collecting like terms, you would have
2j - 4j = 16
-2j = 16
divide both sides by 2
j = 16/(-2)
j = -8
4
ASSIGNMENT (USE YOUR ASSIGNMENT NOTE)
1. James runs 400m every day. Work out how far James runs in one week. Give your
[3 marks]
answer in kilometres.
2. Here is a signpost
Town Center
3.5km
Park
650m
How far apart are the Town Centre and the Park?
Give your answer in kilometres.
(3 marks)
3. A bottle contains 1.75 litres of lemonade.
A can contains 330 ml of lemonade. Phil has 2 bottles of lemonade and 6 cans of
lemonade. How much lemonade does he have in total? Give your answer in millilitres.
Answers
For question 1,
James runs 400m in a day
In a week = 7 days
400m × 7 days = 2800m
To convert 2800m to km
1km = 1000m
So, 2800m/1000m
= 2.8 km
For question 2,
How far are the Town Center and the Park
3.5 km and 650m
650m to km
1km = 1000m
To km = 0.65km
The distance = 3.5km - 0.65km
= 2.85km
So, they are 2.85km apart
For question 3,
A bottle = 1.75 liters of lemonade
A can = 330 ml of lemonade
1.75 liters to milliliters
1 liter = 1000 milliliter
= 1.75 × 1000 ml
= 1750 ml
2 bottles of lemonade
1750ml × 2
= 3500 ml
6 cans of lemonade
330ml × 6
= 1980 ml
In total, 3500ml + 1980ml
= 5480 ml
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(X) 4.7.PS-15
Question Help
A rectangular garden has a walkway around it. The area of the garden is 2(3.5x+2.5). The combined area of the garden and
the walkway is 2.5(6x+4). Find the area of the walkway around the garden as the sum of two terms.
The area of the walkway around the garden is
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Answers
The area of the walkway of the garden is 8x - 15 square units.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
Given, The area of the garden is 2(3.5x + 2.5) and the combined area of the garden and the walkway is 2.5(6x + 4).
Therefore, The area of the walkway is,
= 2.5(6x + 4) - 2(3.5x + 2.5).
= 15x - 10 - 7x - 5.
= 15x - 7x - 10 - 5.
= 8x - 15 square units.
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Rewrite in simplest radical form
Answers
So in simple radical form it is x^(2/3).
2. Order the following decimals from least to greatest.
0.439
0.394
0.441
0.531
0.342
Answers
Answer: 0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
Step-by-step explanation:
0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
If you convert the decimals into fractions out of a hundred, then it will be easily to keep going from least to greatest or greatest to least and soon you won't need help. Keep trying! :)
A pet store has 80
geckos and anole lizards altogether.
The ratio of geckos to anole lizards is 1:3
.
How many geckos does the pet store have?
Answers
Answer:
About 54 geckos
Edward and his little brother made up
a game using coins. They flip the coins
towards a cup and receive points for
every one that makes it in. Edward
starts with 20 points, and his little
brother starts with 18 points. Edward
gets 2 points for every successful
shot, and his brother, since he is
younger, gets 3 points for each
successful shot. Eventually, the
brothers will have a tied score in the
game. How many additional shots will
each brother have made? How many
points will they both have?
Edward and his brother will have each
made ________
shots, for a tied score
of ________
Answers
His little brother made 4
In the figure, ACCB. D is a point on AB such that CD AB.
Prove that x = y.
Answers
Answer: x = y
Step-by-step explanation:
x and y are angles with vertical sides, and angles with vertical sides are always equal
A 35-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $360. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999057. Find the expected value of the policy for the insurance company.
Answers
The expected value of the policy for the insurance company: $359.38
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
The expected value of the policy for the insurance company can be calculated as follows:
Expected value = (Probability of survival) x (Annual payment)
= 0.999057 x $360
= $359.38
So, the expected value of the policy for the insurance company is $359.38.
It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.
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Tina would like to withdraw an annual salary of $35,756 from an account paying 2.2% compounded annually for 35 years once she retires. Given this information, determine the amount needed in her account in order for her to reach her goal. Round to the nearest cent.
Answers
Amount needed in account = Annual salary / (Interest rate / 100)^(Years of compounding)
Amount needed in account = 35756 / (2.2/ 100)^35 Amount needed in account = $737,939.36
This shows a triangle.
7ft
8ft
What is the area of the triangle?
Answers
The area of the given triangle is 28 squared feet
What is the area of a triangleThe area of a triangle is a measure of the amount of space enclosed by the triangle. It is a scalar quantity, meaning that it is a single numerical value with no direction.
The area of a triangle can be calculated using various formulas, depending on the information available about the triangle.
In this problem, we have the value of base and the height of the triangle.
The formula is given as;
A = 1/2 b * h
Substituting the values into the formula;
A = 0.5 * 7 * 8
A = 28 squared feet
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I need help with this question how is dividing with an area model simlar to multiplaying with an area model differnt
Answers
Dividing with an area model and multiplying with an area model are similar in that they both involve partitioning a rectangular area into smaller parts.
However, dividing with an area model involves starting with the total area and then dividing it into equal parts to find the size of each part. For example, to divide 12 by 3, we could draw a rectangle with an area of 12 and then partition it into 3 equal parts to find that each part has an area of 4.
Multiplying with an area model involves starting with the size of the smaller parts and then combining them to find the total area. For example, to multiply 3 by 4, we could draw a rectangle with a width of 3 and a height of 4 and then calculate the area of the rectangle as 12.
So, while both methods involve using an area model, dividing starts with the total area and finds the size of the parts, while multiplying starts with the size of the parts and finds the total area.
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Find the value of z such that 0. 14 of the area lies to the left of z. Round your answer to two decimal places.
Answers
The value of z is -1.09.
The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data collection.
Given: P(Z<z)=0.14
To find the value of z such that 0.14 of the area lies to the left of z.
We will use z-score table to get the value of z here.
IN z-score table, we have
For P(Z<-1.09)=0.14
Hence, the value of z is -1.09.
Its approximate value is -1.09
So the final answer is z=-1.09.
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your father told you that he picked more than 1 apple this year. what is the probability that he picked 3 apples, given that information?
Answers
1) The probability of picking more than 1 apple is 0.8. 2) the expected number of apples you can pick each year is 2.65. 3) the expected number of apples you can pick each year is 2.65.
To find the probability of picking more than 1 apple, we need to find the sum of the probabilities of picking 2, 3, and 4 apples. Using the table, we have P(N>1) = P(2) + P(3) + P(4) = 0.15 + 0.35 + 0.3 = 0.8. So, the probability of picking more than 1 apple is 0.8. The expected number of apples you can pick each year can be calculated using the formula: E(N) = ∑N * P(N), where the sum is taken over all possible values of N. Using the table, we have E(N) = (1 * 0.1) + (2 * 0.15) + (3 * 0.35) + (4 * 0.3) = 0.1 + 0.3 + 1.05 + 1.2 = 2.65. So, the expected number of apples you can pick each year is 2.65. To find the probability of picking 3 apples, given that your father picked more than 1 apple, we need to use the conditional probability formula. We have P(3|N>1) = P(3 and N>1) / P(N>1) = P(3) / P(N>1) = 0.35 / 0.8 = 0.4375. So, the probability of your father picking 3 apples, given that he picked more than 1 apple, is 0.4375
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Complete Question
Imagine you have an apple tree, and you pick apples from it each fall. Empirically, the number of apples (N) that you can harvest and the corresponding probability (P) can be summarized in the following table, the table = N - O, 1, 2, 3, 4 And P = 0.1, 0.15, 0.35, 0.3, 0.1
1) What is the probability that you can pick more than 1 apple? 2) What is the expected number of apples you can pick each year? 3) Your father told you that he picked more than 1 apple this year. What is the probability that he picked 3 apples, given that information?
Find the missing number so that the equation has infinitely many solutions.
– 2x+18=blank x+18
Answers
The missing term in the equation is n = -2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the missing term be represented as n
-2x + 18 = nx + 18
Subtracting 18 on both sides of the equation , we get
-2x = nx
Divide by x on both sides of the equation , we get
n = -2
Therefore , the missing term is n = -2
Hence , the equation is n = -2
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5x-5=3x+15
it’s confusing someone help
Answers
Answer:
x=10
Step-by-step explanation:
First, add 5 to both sides of the equation, getting rid of the -5 on the left side but still making them equal.
5x=3x+20
Then, do the same with 3x, Subtract from both sides.
2x=20
Lastly, Divide both sides by 2 and you'll get your answer
x=10
Answer:
[tex] \sf \: x = 10[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 5x - 5 = 3x + 15
Then the value of x will be,
→ 5x - 5 = 3x + 15
→ 5x - 3x = 15 + 5
→ 2x = 20
→ x = 20 ÷ 2
→ [ x = 10 ]
Hence, the value of x is 10.
thomas think that 3 7/8 +2 11/12 is pretty close to 56 but lorinda thinks it’s is closer to 6. Todd disagree with both of them , and thinks it is closer to 7! what do you think? be clear and complete in you’re response
Answers
Todd has done correct calculation its values is equal to 6.79, which is closer to 7.
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number on the top side, it indicates the number of equal parts taken or whole quantity and denominator is on the bottom side, it indicates the equal parts of the whole quantity.
Given that,
Two fraction numbers in the form of addition,
⇒ 3 7/8 + 2 11/12
It can be further solved as
⇒ (24 + 7)/8 + (24 +11)/12
⇒ 31/8 + 35/12
Now taking LCM of (8, 12)
LCM(8, 12) = 24
making denominator same in the both terms
⇒ 93/24 + 70/24
⇒ 163/24
⇒ 6.79
Thus, the values is closer to 7
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A house has decreased in value by 38% since it was purchased. If the current value is $93,000, what was the value when it was purchased?
Answers
The value of the house when it was purchased was $150,000, before the 38% discount was applied.
A discount is a reduction in price or value, typically given as an incentive to purchase or to compensate for a decline in value.
In this case, we know that the house has decreased in value by 38% since it was purchased. This means that the current value is only 62% of its original value (100% - 38% = 62%).
Now, we can use a proportion to determine the original value of the house. We can set up the equation:
Current value / Original value = 62% / 100%
Substituting the given values, we get:
$93,000 / Original value = 62 / 100
To solve for the original value, we can cross-multiply and simplify:
100 x $93,000 = 62 x Original value
$9,300,000 = 62 x Original value
Dividing both sides by 62, we get:
Original value = $150,000
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Bob bought 40 gumboils from a quarter machine. The number of each flavor he got is shown in the table. If there are 140 gumboils remaining in the machine. what is a reasonable prediction for the number of cola flavored gumboils left?
Answers
Answer: Is only definable if you can show the table but according to a valid explanation it would be most likely 41
Step-by-step explanation:
Lets say Bob has 17 strawberry, 19 Cola, and 4 blueberry, we can infer there is an equal amount of gumballs of each flavor in the machine; Before bob bought any gumballs there were 180 and if there were only 3 flavors we would divide 180 by 3 and get 60. That means each flavor has 60 of its own flavor and if we take 19 from the 60 cola flavored we can get 41.
Please answer it’s for school
Answers
Using the vertices given, the area of triangle PQR is 18 squared units
What is the area of the triangleThe area of triangle PQR can be found using the Shoelace Theorem. This theorem states that the area of a polygon can be calculated by taking the sum of the products of the coordinates of its vertices and subtracting the sum of the products of the coordinates of its vertices in reverse order.
In this case, the vertices of triangle PQR are P(-8, 2), Q(-2, 4), and R(-6, 8), so the area can be calculated as follows:
A = 1/2 * |(-8 * 4) + (-2 * 8) + (-6 * 2) - (2 * -2) - (4 * -6) - (8 * -8)| = 1/2 * |-32 + 16 + -12 - 4 + 24 + 64| = 1/2 * |36| = 18 square units
So the area of triangle PQR is 18 square units.
Learn more on area of triangle here;
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