Using simple interest we know the Total value of annual health coverage is $9000.
What is simple interest?Borrowers must pay lenders simple interest as a fee in exchange for a loan.
Compound interest is excluded from the calculation and just the original principal is used.
Simple interest applies to all loans, not just specific ones.
Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
So, complete yearly health coverage calculation
Let x be the total annual healthcare budget.
Ruth contributes 18% of the entire cost of healthcare, or $67.50 for two weeks. (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
The total amount paid for the entire year is 135 x 12 = 1620.
She foots 18% of the overall annual health care costs, as was already established.
Then,
18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= $9000
Therefore, using simple interest we know the Total value of annual health coverage is $9000.
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Correct question:
Ruth contributes 18% of the total cost of her individual health care. This is a $67.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year?
Please help ASAP. NO LINKS OR FILES I WILL REPORT,
Thank you!
By using Pythagorean theorem, we can find the third side of right angle triangle.
Sin Q = [tex]\frac{PR}{QR}[/tex] = [tex]\frac{14}{50}[/tex] = [tex]\frac{7}{25}[/tex], Cos Q = [tex]\frac{PQ}{QR}[/tex] = [tex]\frac{48}{50}[/tex] = [tex]\frac{24}{25}[/tex], Tan Q = [tex]\frac{PR}{PQ}[/tex] = [tex]\frac{14}{48}[/tex] = [tex]\frac{7}{24}[/tex]
Sin R = [tex]\frac{PQ}{QR}[/tex] = [tex]\frac{48}{50}[/tex] = [tex]\frac{24}{25}[/tex], Cos R = [tex]\frac{PR}{QR}[/tex] = [tex]\frac{14}{50}[/tex] = [tex]\frac{7}{25}[/tex], Tan R = [tex]\frac{PQ}{PR}[/tex] = [tex]\frac{48}{14}[/tex] = [tex]\frac{24}{7}[/tex]
What is Pythagorean theorem?The right triangle's three sides are related in accordance with the Pythagorean theorem, also referred to as Pythagoras' theorem, which is a basic Euclidean geometry principle.
What is Trignometric?Trigonometric refers to the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly the trigonometric functions (sine, cosine, tangent, etc.) that are used to solve problems involving these relationships.
According to given information:
[tex]QR^{2}= PR^{2}+ PQ^{2}[/tex]
[tex]PQ = \sqrt{QR^{2} -PR^{2} }[/tex]
[tex]PQ = \sqrt{50^{2} -14^{2} }[/tex] = 48
Basic Trigonometric formulas,
Sin θ = [tex]\frac{Opposite side}{Hypotenuse}[/tex]
Cos θ = [tex]\frac{Adjacent side}{Hypotenuse}[/tex]
Tan θ = [tex]\frac{Opposite side}{Adjacent side}[/tex]
Sin Q = [tex]\frac{PR}{QR}[/tex] = [tex]\frac{14}{50}[/tex] = [tex]\frac{7}{25}[/tex]
Cos Q = [tex]\frac{PQ}{QR}[/tex] = [tex]\frac{48}{50}[/tex] = [tex]\frac{24}{25}[/tex]
Tan Q = [tex]\frac{PR}{PQ}[/tex] = [tex]\frac{14}{48}[/tex] = [tex]\frac{7}{24}[/tex]
Sin R = [tex]\frac{PQ}{QR}[/tex] = [tex]\frac{48}{50}[/tex] = [tex]\frac{24}{25}[/tex]
Cos R = [tex]\frac{PR}{QR}[/tex] = [tex]\frac{14}{50}[/tex] = [tex]\frac{7}{25}[/tex]
Tan R = [tex]\frac{PQ}{PR}[/tex] = [tex]\frac{48}{14}[/tex] = [tex]\frac{24}{7}[/tex]
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A cab company charges three dollars per cab ride plus an additional two dollar per mile driven how long is a cab ride that cost $9? Right and solve an equation to find the answer
The number of miles that the cab ride that costs $9 is 3 miles.
Let's assume that the length of the cab ride is "x" miles. Then, the cost of the cab ride can be expressed as:
Cost = 3 + 2x
We are given that the cost of the cab ride is $9, so we can set up an equation:
3 + 2x = 9
Subtracting 3 from both sides, we get:
2x = 6
Dividing both sides by 2, we get:
x = 3
Therefore, the length of the cab ride that costs $9 is 3 miles.
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Which expressions represent “the sum of 3 and n”?
Select all that apply
Answer:
Step-by-step explanation:
a- 3+n
Answer:
First option and Second option
Step-by-step explanation:
Hope it helps. Happy Easter Tuesday. Have a great day.
You are trying to help Chantal understand the concept of a 5% slack in the
line. You explain that having a 5% slack means that the length is 5% longer
than it would be if it were completely straight. You compare AABC to Figure
DEF, where curve DE is 5% longer than line segment AB.
Right Triangle without Slack
A
8
B
6
C
Figure with Slack
D
8
E
6
F
Enter the length of curve DE given the curve is 5% longer than line segment
AB.
Thus, the length of the curve DE for the 5% slack in the line is found as :
DE = 10.5 units.
Explain about the percentage increase:The difference in between final number and the original value, stated as a percentage, is known as a percentage increase. To put it another way, the starting value is divided by the difference in between final and initial values, which is then multiplied by 100.
For the given right triangle ABC, applying Pythagorean Theorem:
AB² = AC² + BC²
AB² = 8² + 6²
AB² = 64 + 36
AB² = 100
AB = 10 units
Now, DE is given 5% longer than AB.
DE = AB + 5% of AB
DE = 10 + 5% of 10
DE = 10 + 5*10 / 100
DE = 10 + 0.5
DE = 10.5
Thus, the length of the curve DE for the 5% slack in the line is found as :
DE = 10.5 units.
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Correct question:
You are trying to help Chantal understand the concept of a 5% slack in the
line. You explain that having a 5% slack means that the length is 5% longer
than it would be if it were completely straight. You compare ΔABC to Figure ΔDEF, where curve DE is 5% longer than the line segment AB. Find DE.
Figure is attached.
Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)
SOMEONE HELP ME PLEASE
The estimated probability of an amateur golfer hitting at least 6 times in his next 10 attempts is 20%. The Option A.
What is the estimated probability of an amateur golfer hitting at least 6 times?To simulate the situation, we can use the table of random numbers by selecting the first two digits of each number as a random sample. Let's consider hitting the ball as a success, and missing it as a failure.
So, the amateur golfer has a probability of success of 0.48 and a probability of failure of 0.52. We want to calculate the probability of having at least 6 successes in 10 attempts, which means we need to add up the probabilities of having 6, 7, 8, 9, or 10 successes.
Using binomial probabilities, we can calculate these probabilities as follows:
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10); X is the number of successes in 10 attempts.
Using the binomial formula, we can calculate each probability as:
P(X = k) = (10 choose k) * (0.48)^k * (0.52)^(10-k). By adding up these probabilities, we get P(X ≥ 6) = 0.196 or approximately 20%.
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An airplane is descending to a runway. At an altitude of 15. 2 miles, it’s horizontal distance to the runway is 60 miles. Find the angle of descent
The angle of descent is approximately 18.58 degrees.
A is the airplane, B is the point where it is currently located, C is the point on the runway directly below the airplane, and D is the projection of the airplane onto the ground (i.e. the point directly below the airplane).
We want to find the angle BCD, which is the angle of descent. We can use the tangent function to do this:
tan(BCD) = [tex]\frac{BC}{CD}[/tex]
We know that h = 15.2 miles and x = 60 miles.
To find CD, we need to use similar triangles.
Triangles ABD and BCD are similar, so we can write:
AB/BD = [tex]\frac{DC}{x}[/tex]
Since AB = h and BC = x, we can solve for CD:
h/BD = [tex]\frac{BC}{x}[/tex]
CD = BD *
BD is the distance between the airplane and its projection onto the ground.
Since triangles ABD and BCD are similar, we have:
BD/AB = [tex]\frac{x}{BC}[/tex]
BD/h = [tex]\frac{BC}{DC}[/tex]
BD = h * [tex]\frac{BC}{DC}[/tex]
Substituting CD and BD into the original equation, we get:
tan(BCD) = (h - h * CD / x) x
tan(BCD) = h * (1 - CD / x) x
tan(BCD) = h * (x - CD) (x * CD)
tan(BCD) = h * (x - h * ) / (x * h )
tan(BCD) = CD / (x - h)
tan(BCD) = (h * x / CD) / (x - h)
tan(BCD) = (15.2 * 60 / CD) / (60 - 15.2)
tan(BCD) = 0.3277
Taking the inverse tangent of both sides, we get:
BCD = 18.58 degrees
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state the most specific name of this quadrilateral ....61 points
Answer:Kite
Step-by-step explanation:
Because according to the diagram the shape has 2 pairs parallel sides and that is also 1 of the properties of a kite
so when identifing a shape look and the details of the shape like the broken lines to signify a diagonal equal sies and so on
hope this helps
Sarah and Nathan each picked a bucket of strawberries. Sarah picked 4 pounds, and Nathan picked 3 pounds. How much more did Sarah pick than Nathan?
1 1/2 pounds
2 pounds
1 pound
1/2 pound
Therefore , the solution of the given problem of fraction comes out to be "1 pound" is the right response.
A fraction is what?Any combination of sections of the same size can be used to represent the whole. Quantity is described as "a portion" under a particular measurement in Standard English. 8, 3/4. Fractions are included in wholes. These act as the ratio divisor, which is a pair of integers in mathematical words. Here are a couple of examples showing how to change straightforward halves into entire numbers.
Here,
Nathan picked 3 pounds of strawberries compared to Sarah's 4 pounds. We can deduct Nathan's picking from Sarah's picking to see how much more Sarah picked than Nathan.
=>Sarah's picking and Nathan's picking =
=> 4 pounds - 3 pounds = 1 pound, respectively.
This means that Sarah harvested 1 pound more strawberries than Nathan did.
Therefore, "1 pound" is the right response.
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_____ show the change in one or more variables progressively across time. a. Histograms b. Pie charts c. Line graphs d. Bar charts e. Diagrams.
The correct answer is c. Line graphs show the change in one or more variables progressively across time.
Histograms show the distribution of data, pie charts show the proportions of a whole, bar charts compare categories or groups, and diagrams show the relationships between different elements.
The correct answer is c. Line graphs show the change in one or more variables progressively across time
A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics. Frequency, which can be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data.
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Line graphs show the change in one or more variables progressively across time. C
A line graph is a type of chart that displays data as a series of data points connected by straight lines.
The horizontal axis of the graph typically represents time, while the vertical axis represents the value of the variable being measured.
By connecting the data points with lines, a line graph can show the trend or pattern of change in the variable over time.
Line graphs are commonly used in fields such as economics, finance, and science to visualize trends in data over time.
They can be used to identify patterns, compare different variables, or forecast future trends.
In contrast, histograms, pie charts, bar charts, and diagrams are different types of charts that are used to display data in different ways.
Histograms are used to show the distribution of data within a single variable, while pie charts and bar charts are used to compare different categories or groups of data.
Diagrams are used to represent complex systems or relationships, often using visual symbols or icons to represent different components.
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Simplify. 11 3/4-8 1/2
Therefore, 11 3/4 - 8 1/2 = 13/4, or 3 1/4 as a mixed number.
What is mixed number?A mixed number is a type of number that represents a whole number and a fraction together. It is written in the form of a whole number followed by a fraction, such as 3 1/2. The whole number represents the number of whole units, while the fraction represents the part of a unit.
For example, the mixed number 3 1/2 can be interpreted as three whole units and one half of a unit. Another example of a mixed number is 2 3/4, which represents two whole units and three-quarters of a unit. Mixed numbers are commonly used in everyday life, such as in cooking and measuring, and in mathematical calculations involving fractions.
To subtract mixed numbers like these, we need to convert them to improper fractions first:
[tex]11 3/4 = (4 * 11 + 3)/4 = 47/4[/tex]
[tex]8 1/2 = (2 * 8 + 1)/2 = 17/2[/tex]
Now, we can subtract the fractions:
[tex]47/4 - 17/2[/tex]
To subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 2 is 4 × 2 = 8. We can convert both fractions to have a denominator of 8:
[tex]47/4 = (47/4) * (2/2) = 94/8[/tex]
[tex]17/2 = (17/2) * (4/4) = 68/8[/tex]
Now, we can subtract the numerators:
[tex]94/8 - 68/8 = 26/8[/tex]
Finally, we can simplify the result by dividing both numerator and denominator by their greatest common factor, which is 2:
[tex]26/8 = (2 * 13)/(2 * 4) = 13/4[/tex]
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unit 8 homework 4 numbers 11 and 13
Step-by-step explanation:
how could you solve 10., if you cannot solve 11. ? they are using the same thing : law of sine.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c being the sides, and A, B, C being the corresponding opposite angles.
11.
x/sin(90) = 13/sin(70)
as sin(90) = 1
x = 13/sin(70) = 13.83431104...
13.
remember, the sum of all angles in a triangle is always 180°.
angle JLM = 180 - 90 - 51 = 39°
angle LJK = 180 - 90 - 72 = 18°
14/sin(39) = JL/sin(51)
JL = 14×sin(51)/sin(39)
JL/sin(90) = JL = 14×sin(51)/sin(39) = KL/sin(18)
KL = 14×sin(51)×sin(18)/sin(39) = 5.342458907...
morbidity surveys of the general population: group of answer choices include the health and nutrition examination survey. all of these are correct. collect data on the health status of a population group. typically use a scientifically designed representative sample.
In morbidity surveys of the general population, they collect data on the health status of a population group which includes the health and nutrition examination survey, that are typically uses a scientifically designed representative sample. So the answer is all of these are correct or option B.
What are Morbidity Surveys?
Morbidity surveys are research investigations designed to determine the frequency and incidence of diseases, illnesses, and injuries in a certain community. They are intended to collect data on people's health status within a certain community or population, as well as to determine the distribution and drivers of health issues in that group.
Morbidity surveys often employ structured questionnaires and physical examinations to gather data on the occurrence of certain health disorders, as well as risk factors and other variables that may be related to the development of these illnesses.
Morbidity survey data may be used to design public health policies and programs, distribute resources, and track changes in health status over time.
The answer is (b) All of these are correct.
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Health surveys provide a structured way to collect and interpret data about the health status of a population, helping researchers and policy makers understand health trends and conditions. One such survey is the Health and Nutrition Examination Survey.
Explanation:Surveys, such as the Health and Nutrition Examination Survey, provide an important method for collecting data on the health status of a population group. In public health and epidemiology, these surveys typically use a scientifically designed representative sample to provide accurate data. To conduct this survey, researchers ask the same questions to all respondents, interpret the answers, and tabulate the results. A simple example could be comparing the eating habits of students eating off campus versus those in dining facilities. With the data gathered, we can identify health trends, understand the distribution of certain health conditions, and then make informed policy or healthcare decisions based on these insights.
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pls helpppp with this
Answer:
[tex]y = 2x - 1[/tex]
Step-by-step explanation:
We can represent this line in an equation in slope-intercept form:
[tex]y = mx + b[/tex],
where [tex]m[/tex] is the line's slope (rise over run), and [tex]b[/tex] is the y-coordinate of its y-intercept.
First, we can solve for the line's slope:
slope = rise / run = 2/1 = 2
Next, we can identify the y-coordinate of the y-intercept by looking at the vertical axis' value when the red line crosses it:
-1
Finally, we can put these two pieces of information together to form an equation in slope-intercept form:
[tex]\boxed{y = 2x - 1}[/tex]
52 no one can win more than one prize? multiple choice 16,129,423 16,497,400 15,281,283 16,300,400
The closest choice to the actual number of ways to choose 52 different winners out of 52 contestants is 16,497,400,
To solve this problem, we can use the formula for permutations, which is:
nPr = n! / (n - r)!
where n is the total number of objects (in this case, 52), and r is the number of objects we are choosing (in this case, the number of prizes, which is also 52).
Since no one can win more than one prize, we need to choose 52 different winners for the prizes. Therefore, the number of ways to do this is:
52P52 = 52! / (52 - 52)! = 52!
Using a calculator or computer program, we can find that 52! is approximately equal to 8.0658 × 10^67.
Therefore, the answer is 16,497,400, which is the closest choice to the actual number of ways to choose 52 different winners out of 52 contestants.
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If cosθ=-3/4 and tanθ is negative find sinθ
If cosθ=-3/4 and tanθ is negative, then sinθ= √(7)/4.
Since cosθ = -3/4 and θ is an angle in the second quadrant where cosθ is negative, we know that sinθ must be positive.
The Pythagorean identity is a trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent
To find sinθ, we can use the Pythagorean identity
sin^2θ + cos^2θ = 1
Substituting the value of cosθ we get
sin^2θ + (-3/4)^2 = 1
Simplifying
sin^2θ + 9/16 = 1
sin^2θ = 7/16
Taking the square root of both sides, we get
sinθ = ±√(7)/4
Since we know that sinθ is positive in the second quadrant, we take the positive value
sinθ = √(7)/4
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there are four blood types, and not all are equally likely to be in blood banks. in a certain blood bank, 49% of donations are type o blood, 27% of donations are type a blood, 20% of donations are type b blood, and 4% of donations are type ab blood. a person with type b blood can safely receive blood transfusions of type o and type b blood. what is the probability that the 4th donation selected at random can be safely used in a blood transfusion on someone with type b blood? ( to the nearest thousandth)
The probability that the fourth donation selected at random can be safely used in a blood transfusion on someone with type B blood is 0.69.
How to find the probability?Since a person with type B blood can safely receive blood transfusions of type O and type B blood, the fourth donation selected at random must be either type O or type B blood. From the information given, the probability of the fourth donation being type O blood is 49%, and the probability of it being type B blood is 20%. Therefore, the probability that the fourth donation can be safely used in a blood transfusion on someone with type B blood is:
P(type O or type B) = P(type O) + P(type B) = 0.49 + 0.20 = 0.69
So, the probability that the fourth donation selected at random can be safely used in a blood transfusion on someone with type B blood is 0.69 (rounded to the nearest thousandth).
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g which test would you perform? choice 1 of 4:anova choice 2 of 4:tukey's hsd choice 3 of 4:wilcoxon rank sum test choice 4 of 4:wilcoxon sign rank test
I would perform the ANOVA test (choice 1 of 4).
How to determine if there are significant differences between the means of three or more groups?I would perform the ANOVA test (choice 1 of 4). The ANOVA test is used to test the null hypothesis that the means of all groups are equal, and if the test results in a significant p-value, it suggests that at least one of the group means is significantly different from the others.
Tukey's HSD test (choice 2 of 4) is a post-hoc test that can be used after an ANOVA test to determine which specific groups differ significantly from each other.
The Wilcoxon rank-sum test (choice 3 of 4) is a non-parametric test used to compare the medians of two independent groups.
The Wilcoxon signed-rank test (choice 4 of 4) is a non-parametric test used to compare the medians of two related groups (i.e., paired or matched samples).
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A, B & C form the vertices of a triangle, where
∠
CAB = 90°.
AB = 10.6 m and AC = 5.8m.
Evaluate
∠
ACB, giving your answer rounded to 3 SF.
Answer:
We can use the trigonometric function of sine to find the measure of angle ACB.
First, we note that sin(ACB) = opposite/hypotenuse = BC/AB.
To find BC, we use the Pythagorean theorem:
BC^2 = AB^2 - AC^2
BC^2 = (10.6 m)^2 - (5.8 m)^2
BC^2 = 67.24 m^2 - 33.64 m^2
BC^2 = 33.6 m^2
BC = sqrt(33.6) m
BC = 5.8 m (rounded to 1 decimal place)
Therefore, sin(ACB) = BC/AB = 5.8/10.6 = 0.5472
Using the inverse sine function on a calculator, we find:
ACB = sin^-1(0.5472)
ACB = 33.11°
Therefore, the measure of angle ACB is 33.11 degrees, rounded to 3 significant figures.
Find the nearest 10th the cylinder is 22 inches and 12.5 inches what is the lateral surface ?
Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².
What is surface area?Surface area is the total area of the exposed surfaces of a three-dimensional object. It is measured in square units such as square centimeters (cm2) or square meters (m2). Surface area is an important concept in mathematics, science, and engineering, as it is the total area that determines properties such as friction, heat transfer, and fluid dynamics. For example, a larger surface area can increase the rate of heat transfer and allow for more efficient cooling. Similarly, a larger surface area can increase the friction between two objects, allowing them to grip better. Surface area is also important in chemistry, as it affects the amount of gas or liquid that can be absorbed or released by a given object.
The cylinder has a radius of 11 inches and a height of 12.5 inches. To find the lateral surface area of a cylinder, the formula used is A = 2πrℎ, where r is the radius and h is the height of the cylinder. After plugging in the values, the lateral surface area of the cylinder is 821.75 inches². Rounding the result off to the nearest 10th, the lateral surface area of the cylinder is 822 inches².
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Which of the following best describes the z-score?
A) It is the difference between the median and the mean.
B) It is how many standard deviations a value is from the mean.
C) It is the area under the curve for one standard deviation.
D) Negative z-scores correspond to negative areas.
Answer:
Step-by-step explanation:h
Which equation is equivalent to 60% of 25? Select all that apply.
A. 0. 6 • 25 = x
B. X• 1. 6 =25
C. 6/10 = x/25
D. 60/100 = 25/x
E. X/25 = 60/100
F. 6. 0 • 25=x
Answer:
The equation which is equivalent to 60% of 25 is x = 0.6 * 25
An equation is used to show the relationship between variables, numbers.
Let x represent the value of 60% of 25. Hence:
x = 60% of 25
x = 0.6 * 25
Hence the equation which is equivalent to 60% of 25 is x = 0.6 * 25
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Answer:
A. 0.6 • 25 = 15
C. 6/10 = x/25 => 6/10 * 25 = 15 = x
E. X/25 = 60/100 => X = (60/100) * 25 = 15
So the equations that are equivalent to 60% of 25 are A, C, and E.
Step-by-step explanation:
2. Eh Kaw owns The Donut Hole, currently valued at $115,000. Determine the value of the business in 2 years if Eh Kaw predicts
12% growth.
$146,843.50
$152,666.20
$161,566.72
$144,256.00
the value of The Donut Hole in two years with a 12% growth rate would be $152,666.20
How to solve the question?
To determine the value of The Donut Hole in two years with a 12% growth rate, we can use the formula for compound interest:
A = P*(1+r/n)^(n*t)
where A is the future value, P is the present value, r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $115,000, r = 0.12, n = 1 (compounded annually), and t = 2.
Plugging in these values, we get:
A = $115,000*(1+0.12/1)₁₂
A = $115,000(1.12)²
A = $152,666.20
Therefore, the value of The Donut Hole in two years with a 12% growth rate would be $152,666.20.
It's important to note that this is a rough estimate and assumes that the business will continue to grow at a steady rate without any significant changes in the market or the business itself. It's also possible that the actual value could be higher or lower depending on various factors.
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A chef used some bouillon cubes when making chicken noodle soup. The volume of each of the bouillon cubes was 1/27
cubic inch. How long was an edge of one of the bouillon cubes that the chef used?
Answer: 1/3
Step-by-step explanation:
1/3x1/3x1/3=1/27
A circle with center O(2, 3) contains the point A(5, 11).
The equation of the circle is x² + y² - 4x - 6y - 60 = 0
Equation of a circle :The equation of a circle is generally given by the formula:
=> (x - a)²+ (y - b)² = r²
Where (a, b) is the center of the circle, and r is its radius. The equation describes all the points (x, y) in the xy-plane that are a fixed distance r from the center point (a, b).
Here we have
A circle with centre O(2, 3) contains the point A(5, 11).
Since point A(5, 11) is located on the circle with center O(2, 3), use the distance formula to determine whether A is actually on the circle.
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
=> d = √(x₂ - x₁)² + (y₂ - y₁)²)
Using this formula, the distance between O(2, 3) and A(5, 11) is:
d = √(5 - 2)² + (11 - 3)²)
= √(3² + 8²)
= √(9 + 64)
=√(73)
This distance is the radius of the circle with center O.
Therefore, the equation of the circle is:
(x - 2)² + (y - 3)² = (√(73))²
x² - 4x + 4 + y² - 6y + 9 = 73
x² + y² - 4x - 6y - 60 = 0
Therefore,
The equation of the circle is x² + y² - 4x - 6y - 60 = 0
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What is the exact area of the trapezoid?
Answer:
135.07 mm2
Step-by-step explanation:
height = 10.39 mm
area = 135.07 mm2
Solve the equation A = bh for b.
b = Ah
b = A/h
b=h/A
b=h-A
DONE
Solve the equation A =
Ob₁ = 2A/h-b₂
b₁ = A/h - 2b2
Ob₁ = 2h/A-2b2
b₁ = A-hb₂
DONE
h(b₁ + b₂)
2
for b₁-
Answer:
Starting with the given equation:
Ob₁ = 2h/A - 2b₂
We want to solve for b₁. First, we can simplify the equation by multiplying both sides by 2:
2Ob₁ = 4h/A - 4b₂
Next, we can add 4b₂ to both sides to isolate the term involving b₁:
2Ob₁ + 4b₂ = 4h/A
Then, we can multiply both sides by A/4h to solve for b₁:
b₁ = (2Ob₁ + 4b₂) * A/4h
Simplifying this expression, we get:
b₁ = (O/h + 2b₂) * A/2
Therefore, the solution for b₁ is:
b₁ = (O/h + 2b₂) * A/2
or
b₁ = (A O + 2b₂h)/2h
In the equation A=bh, b can be solved as b=A/h. For the equation h(b₁ + b₂)=2, b₁ can be solved as b₁=2/h-b₂
Explanation:To solve the equation A = bh for b, we can isolate b by dividing both sides of the equation by h. Thus, b = A/h. For the equation h(b₁ + b₂) = 2, we isolate b₁ by first dividing both sides by h to get (b₁ + b₂) = 2/h. Then, we can subtract b₂ from both sides to solve for b₁, yielding b₁ = 2/h - b₂.
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What is the value of x in this triangle?
x=47°
The degree of a triangle is equal to 180°.
Since a triange=180°, you would subtract 180 by 102+31 because the other two angles are 102° and 31°.
180-102-31=47°
Therefore the answer would be x=47°
you want to rent an unfurnished one-bedroom apartment for next semester. the mean monthy rent for a random sample of 45 apartments advertised in the local newspaper is $775. assume the standard deviation is $110. find a formula used to generate the 98% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.
Formula:
98% Confidence Interval = (Mean - (2*Standard Deviation/√n), Mean + (2*Standard Deviation/√n))
98% Confidence Interval = ($775 - (2*$110/√45), $775 + (2*$110/√45))
98% Confidence Interval = ($735.56, $814.44)
What is the most upper (+3) or (-7)? Help please
Answer: Of the two numbers you provided, +3 is greater than -7. So, +3 is the most upper of the two numbers.
Answer: +3
Step-by-step explanation: Positive 3 is greater than negative 7. Therefore, +3 is the greater value.
