The value of the shortest of the three side lengths is 3 inches.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The lengths of the three sides of a triangle (in inches) are consecutive integers.
The three sides are x, x+1 and x+2 which are consecutive.
We know that perimeter of a triangle is the sum of the three sides of a triangle.
Add the three Consecutive sides to find the perimeter.
Perimeter of triangle=x+x+1+x+2
The perimeter of triangle is 27 inhces.
27=3x+3
Substitute 3 from both sides
24=3x
Divide by 3 on both sides
8=x
Hence, the value of the shortest of the three side lengths is 3 inches.
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What is the equation of the line that passes through the point (4,1) and (8, -4)?
Answer:
y= -5/4x+
Step-by-step explanation:
find the gradient first ∆y/∆5x
-4-1/ 8-4
=-5/4
assume one of the points to be x, y
y-1/ x-4 =-5/4
cross multiply
4y-4=-5x+20
4y= -5x+20+4
divide both sides by 4
y= -5/4x+
Find the exact value of sin V in simplest radical form.
√74
7
The exact value of sin V in simplest radical form is 0.813.
What is law of sines?
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
Given;
Sin ratio √74:7
Now,
AB/sinA=BC/sinB
√74/sinA = 7/sinB
√74/sin90 = 7/sinB
sinB=7/√74
sinB=0.813
Therefore, the answer of sin V will be 0.813.
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The difference between a two-digit number and the reverse of the number is 18. What could the original number be if the reversed number is also a two-digit number? List all possibilities.
pls answer by sunday february 12, 12:00 p.m. , pacific standard time!
Answer:
27, 36
Explanation:
To find the possible two-digit numbers that meet the criteria, we can use algebra. Let x be the original two-digit number, and let y be the reverse of x. Then, we have:
x - y = 18
We can also write y in terms of x:
y = x % 10 * 10 + x / 10
Substituting the expression for y into the equation x - y = 18, we get:
x - (x % 10 * 10 + x / 10) = 18
Expanding and simplifying the right side of the equation, we get:
9x = 180 + 10
Dividing both sides of the equation by 9, we get:
x = 20
Since x must be a two-digit number, 20 is not a valid solution. However, we can check the two numbers that are close to 20, which are 18 and 21.
For x = 18, we have y = 81, which is a two-digit number, so 18 is a valid solution.
For x = 21, we have y = 12, which is a two-digit number, so 21 is also a valid solution.
Therefore, the possible two-digit numbers that meet the criteria are 27 and 36.
Solve for x.
9/3 = x/2
[tex] \frac{9}{3} = \frac{x}{2} \\ [/tex]
Cross multiply...
[tex]3x = 18[/tex]
[tex]x = \frac{18}{3} \\ [/tex]
x = 6
Answer:
it's 6. 9 is divided by 3 and the answer is 3 .so 3=x÷2. and multiplie 2 in both side.so the answer is 6.
Find the measures of each interior angles of a regular polygon having 15 sides
The measure of each interior angle of a regular polygon having 15 sides is equal to option B: 156°.
A polygon is an enclosed figure composed of more than three straight lines. To find the measure of each interior angle of a regular polygon having n sides, we would first find the total sum of interior angles of this polygon. The formula is:
(n-2) × 180°
= (15-2) × 180°
= 13 × 180°
= 2340°
We, here, found that the sum of all interior angles of a regular polygon having 15 sides is equivalent to 2340°. Now, to find the measure of each angle, we can divide this sum by the number of sides as:
2340/15 = 156°.
Therefore, the measure of each angle of a regular polygon having 15 sides is equivalent to 156°.
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Complete question is:
Find the measures of each interior angles of a regular polygon having 15 sides.
A. 106°
B. 156°
C. 206°
D. 256°
You’ve saved $45, which is 70% of the amount you want to save. What is the total amount you want to save? (round to nearest cent) * *
Rounding this to the nearest cent, the total amount that was wanted to be saved is $64.29.
To solve this problem, we can set up a proportion using the given information. Let x be the total amount that was wanted to be saved.
We know that the amount saved ($45) is 70% of the total amount that was wanted to be saved. Therefore, we can write:
45 = 0.7x
To solve for x, we can divide both sides by 0.7:
x = 45 ÷ 0.7
x = 64.28571429
The answer to the problem is $64.29, rounded to the nearest cent. This means that the total amount that was wanted to be saved was $64.29, and 70% of this amount is equal to the amount that was actually saved ($45). To check our work, we can multiply 64.29 by 0.7 to see if it equals 45. When we do this, we get:
64.29 x 0.7 = 45.003, which rounds to $45, so our answer is correct.
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maths grade 8 cbse...
The value of the expression is 5.
What is order of operations?
The order of operations is a rule that specifies the correct sequence of steps to be taken when evaluating a mathematical equation.
To simplify this expression, we need to follow the order of operations, which is:
Exponents (powers, roots)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
So, we start with the exponents:
[tex]3^0+4^{-1} \\= 1 + 1/4 \\= 5/4[/tex]
Now we substitute this value back into the original expression:
[tex](3^0+4^{-1} )*2^2\\ = (5/4) * 2^2 \\= (5/4) * 4 \\= 5[/tex]
Therefore, the value of the expression is 5.
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for damian's lemonade recipe, 6 lemons are required to make 5 cups of lemonade. at what rate are lemons being used in cups of lemonade per lemon?
The rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon
To find the rate at which lemons are being used in cups of lemonade per lemon, we need to divide the number of cups of lemonade produced by the number of lemons used.
In this case, 5 cups of lemonade are produced from 6 lemons, so the rate at which lemons are being used in cups of lemonade per lemon is:
5 cups of lemonade ÷ 6 lemons = 0.83 cups of lemonade per lemon (rounded to two decimal places)
the rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon
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Solve for x. Round to the nearest tenth,if necessary.
The value of x is approximately 0.8 cm when rounded to the nearest tenth.
Describe Triangle?A triangle is a two-dimensional geometric shape that has three sides and three angles. It is the simplest polygon and is a fundamental building block in many areas of mathematics and science.
The three sides of a triangle can have different lengths and can be of different types, such as equilateral, isosceles, or scalene. An equilateral triangle has three sides of equal length, while an isosceles triangle has two sides of equal length and a third side of a different length. A scalene triangle has all three sides of different lengths.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Thus, we have:
sin(IHJ) = IJ/IH
Taking the sine of both sides and substituting the given values, we get:
sin(23°) = x/2
Multiplying both sides by 2, we have:
x = 2*sin(23°)
Using a calculator, we get:
x ≈ 0.83
Therefore, the value of x is approximately 0.8 cm when rounded to the nearest tenth.
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what is 2+4x6 in math and english
Answer:
Step-by-step explanation:
4 x 6= 24
24+2=26
what is the correct decision in a hypothesis if the data produce a t-statistic that is in the critical region?
The correct decision in a hypothesis test when the data produces a t-statistic that is in the critical region is to reject the null hypothesis.
This is because a t-statics in the critical region indicates that the differences between the sample mean and the population mean are statistically significant. This means that the data indicates that the null hypothesis is wrong and that the alternative hypothesis is true. In a hypothesis test, the null hypothesis is what the researcher is trying to disprove. It is the general statement that suggests that there is no difference between the sample mean and the population mean. The alternative hypothesis is what the researcher is attempting to prove. It suggests that there is a difference between the sample mean and the population mean. Therefore, when the data produces a t-statistic that is in the critical region, it indicates that the alternative hypothesis is true. When a t-statistic is in the critical region, it means that the result is statistically significant. This means that the differences between the sample mean and the population mean are unlikely to have occurred by chance and that the alternative hypothesis is likely to be true. Therefore, when the data produces a t-statistic that is in the critical region, the correct decision is to reject the null hypothesis and accept the alternative hypothesis.
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You teach an arts and crafts class at your local library. There are 12 girls and 11 boys registered for the class. You
need to purchase supplies that will cost $5 per student.
How much will it cost to purchase the supplies?
$28
$67
$71
$115
$192
Answer:
$115
Step-by-step explanation:
12 + 11 = 23
There are 23 students in the class.
Cost of supplies: $5 per student.
total cost = 23 × $5 = $115
The total cost to purchase the supplies is,
⇒ $115
What is mean by Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
There are 12 girls and 11 boys registered for the class.
And, You need to purchase supplies that will cost $5 per student.
Here, Total students = 12 + 11 = 23
Hence, The total cost to purchase the supplies is,
⇒ 23 x $5
⇒ $115
Thus, The total cost to purchase the supplies is,
⇒ $115
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What is the area of KELP, h = 52.6, b1 = 47.8, b2 = 39.1 *
A diagram with Trapezoid KELP and Circle C is shown. Given the dimensions, find the
area of each figure and complete the table. Round to the nearest hundredth if
necessary.
The area of the trapezoid KELP is approximately 2285.47 square units.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
The formula to find the area of a trapezoid is -
A = (1/2) × h × (b1 + b2)
where -
A is the area of the trapezoid.
h is the height of the trapezoid.
b1 and b2 are the lengths of the parallel bases of the trapezoid.
Using the given values, we can substitute them into the formula and solve for the area -
A = (1/2) × h × (b1 + b2)
A = (1/2) × 52.6 × (47.8 + 39.1)
A = 2285.47
Therefore, the area value is 2285.47 square units.
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Dena cuts wood for a treehouse. She has 5 pieces of wood left over with the following lengths in centimeters: 12.7, 26 3/10, 15 4/5, 21 1/4, and 19.2.
A. Write and evaluate an expression to find the total length of wood left over.
______________________________________________________________
B. Dena wants to make a birdhouse with the leftover wood. She needs 105 3/5 centimeters of wood for the birdhouse. Write and evaluate an expression to determine how much more wood will be needed.
______________________________________________________________
7. 3 You are presented with three coins. You are told that two of them are fair, meaning thatif flipped, they will return heads or tails with a 0. 5 probability. You are also told that one isweighted, and will return heads 0. 8 of the time and tails 0. 2. You pick one coin arbitrarilyand flip it; it returns heads. Calculate the probability that the coin you are holding is theweighted one, given that it returned heads on one flip
The probability of the coin being the weighted one given that it returned heads is 0.8.
P(Weighted | Heads) = ( P(Heads | Weighted) * P(Weighted) ) / P(Heads)
= ( 0.8 * 0.5 ) / 0.5
= 0.8
The probability of the coin being the weighted one given that it returned heads can be calculated using Baye's Theorem. This theorem states that the probability of an event given a condition is equal to the probability of the condition given the event multiplied by the probability of the event divided by the probability of the condition. In this case, the event is the coin being weighted, the condition is the coin returning heads. Therefore, the probability of the coin being the weighted one given that it returned heads is equal to the probability of the coin returning heads given that it is weighted multiplied by the probability of the coin being weighted divided by the probability of the coin returning heads. The probability of the coin returning heads given that it is weighted is 0.8, the probability of the coin being weighted is 0.5, and the probability of the coin returning heads is 0.5. Thus, the probability of the coin being the weighted one given that it returned heads is 0.8.
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Find the area and circumference of each circle.
The area and circumference of each circle are 78.5cm², 31.4cm, 113.04cm², 37.68cm, 28.26cm², 18.84cm and 153.86cm², 43.96cm respectively
What is the area of a circleUsing the formula of area of a circle and circumference of a circle, we can solve for each circle as
a.
The area is given as;
A = πr²
A = 3.14 * 5²
A = 78.5cm²
The circumference = 2πr
C = 2 * 3.14 * 5 = 31.4cm
b
A = πr²
A = 3.14 * 6²
A = 113.04cm²
C = 2πr
C = 2 * 3.14 * 6
C = 37.68cm
c.
A = πr²
A = 3.14 * 3²
A = 28.26cm²
C = 2 * 3.14 * 3
C = 18.84cm
d.
A = πr²
A = 3.14 * 7²
A = 153.86cm²
C = 2πr
C = 2 * 3.14 * 7
C = 43.96cm
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How many times dose 6 go into 18
Answer:
3 times
Step-by-step explanation:
6 x 3 = 18
Answer:
3
Step-by-step explanation:
18/6 = 3
or
6 + 6 + 6 = 18
(x + 1) /x³ − 3x² + 6x +11.
The polynomial expression cannot be divided
How to divide the polynomial expressionFrom the question, we have the following parameters that can be used in our computation:
(x + 1) /x³ − 3x² + 6x +11.
The degree of the numerator is 1
While the degree of the denominator is 3
For a polynomial quotient to be evaluated, the degree of the numerator must be greater than the degree of the denominator
Because 1 is less than 3, then the polynomial expression cannot be divided
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Andre luke and shemai had 1400 marbles. If andre had 200 fewer than luke and twice as many as shemai. How many did luke receive
Luke received a total of 640 marbles from the total of 1400 marbles that Luke, Andre and Shema had combined.
Luke, Shemai and Andre combined has 1400 marbles. Andre has 200 fewer than Luke and twice as many as Shemia.
Now, let us say that Luke had X marbles then Andre will have X-200 marble and Shemai will have X/2 marbles.
Now, all the marbles combined will be equal to 1400, so, the simple algebraic relation will be,
X + X-200 +X/2 = 1400
X+X+X/2 = 1600
5X/ = 3200
X = 640
So, Luke will have a total of 640 marble while Andre and Shemai will have 440 and 320 marbles each.
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Reeta has spent 2/7 of her salary on car repair work. She has 15. 000 rupees left with her. What is her salary?
As per unitary method, Reeta's salary is 21,000 rupees.
The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.
In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.
Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:
2/7 * x
Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:
2/7 * x = x - 15,000
Simplifying this equation, we get:
2x = 7(x - 15,000)
2x = 7x - 105,000
5x = 105,000
x = 21,000
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A truck travels from a factory to a gas station in 3 minutes. It stops at the gas station for 2 minutes. The truck then returns to the factory in 5 minutes. Which graph best represents the distance, y, in miles, of the truck from the factory after a certain amount of time, x, in minutes?
Group of answer choices
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 2, 3. The second straight line joins 2, 3 and 5, 3, and the third straight line joins ordered pair 5, 3 with the ordered pair 10, 0.
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3 and 5, 3, and the third straight line joins ordered pair 5, 3 with the ordered pair 10, 0.
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3 and 6, 3, and the third straight line joins ordered pair 6, 3 with the ordered pair 10, 0.
A graph shows Time in minutes along the x-axis and Trucks distance from factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 2, 3. The second straight line joins 2, 3 and 4, 3, and the third straight line joins ordered pair 4, 3 with the ordered pair 10, 0.
Answer:
Step-by-step explanation:
A graph shows Time in minutes along the x-axis and the Truck's distance from the factory in miles along the y-axis. The scales on the x- and y-axes are from 0 to 10 at increments of 1. There are three straight lines in the graph. The first line joins the ordered pair 0, 0 with 3, 3. The second straight line joins 3, 3, and 5, 3, and the third straight line joins ordered pairs 5, 3 with the ordered pair 10, 0.
The rate per cent per annum at which
$1200 is invested to gain $ 72 in simple
interest in three years is
(A) ½
(B) 2
(C)
(D)
9¹/2
18
Dr. Grumman got his first job in 2020. In that year, the government took out 6.2% of a person's
income for Social Security, until a person made $137,700. If Dr. Grumman earned $141,340 in
2020, how much did he pay to Social Security?
The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
What are percentages?A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Formula for percentages: (Value/Total value) * 100
Dr. Grumman earned $141,340 in 2020.
The social security he paid is:
(141340)(6.2/100) = 8763.08
Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.
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Can Someone tell me the answer for this one pleas:
Determine which integers in the set S:{−4, 4, 6, 21} make the inequality 3(j − 5) > 3(7 − 2j) true.
S:{6, 21}
S:{4, 21}
S:{−4, 6}
S:{−4, 4}
The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.
An inequality response is defined?
An expression in mathematics where the sides are not equal is referred to as being inequal. A comparison of any two values, known as an inequality, demonstrates that one value is less than, larger than, or equal to the value on the opposite side of the equation.
The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.
First, we will simplify the given inequality.
3(j-5)>3(7-2j)
⇒j-5>7-2j
⇒3j>12
⇒j>4
It means that numbers greater than 4 will satisfy the given inequality.
Numbers greater than 4 in the given set are 6,21.
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which statement justifies step three? Which statement justifies step four?
Given: AB=AD;BC=DC
Prove:
The two statements that justifies step three and four in the congruency proof are;
Reason 3: SSS Congruency Postulate
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
How to Identify the Congruency Proof?The two column proof is as follows;
Statement 1: AB ≅ AD, BC ≅ DC
Reason 1: Given
Statement 2: AC ≅ AC
Reason 2: Reflexive Property of Congruence
Statement 3: ΔABC ≅ ΔADC
Reason 3: SSS Congruency Postulate
Statement 4: ∠ABC ≅ ∠ADC
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
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What point lies on the line with a slope of m=2/3 that passes through the point (-3,-2)?
PLEASE SHOW WORK
Answer: y = 2/3x
Step-by-step explanation:
This is pretty easy too
the equation for a line is: y = mx + b, where m is the slope and b is the y intercept
y = 2/3x + b, where we need to find b
substituting the point we are given:
-2 = 2/3(-3) + b
-2 = -2 + b
0 = b
so our line is simply:
y = 2/3x
the average number of dropout for a school dsitrict has been 305 per year with a standard eveiation of 50. what is the probility that the number of dropouts next year will be: g
The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.
Probability of dropouts next year being exactly 305: 0
Probability of dropouts next year being less than 305: 0.68
Probability of dropouts next year being greater than 305: 0.32
Probability of dropouts next year being within one standard deviation of 305: 0.95
The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.
The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.
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he accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency.
a) Which would you expect to be larger: the median or the mean? Explain briefly.
b) Which would you report: the median or the mean? Explain briefly.
a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.
a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.
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solve the right triangle by completing the table below :) help asap
The missing sides of the two right triangles are B ≈ 75.5, b ≈ 10.7 and a ≈ 6.9.
How to find the missing sides of a system formed by two similar right triangles
In this problem we find two similar right triangles. Two triangles are similar when they have congruent angles and sides that are not congruent but proportional. Sides in right triangles are related each other by means of Pythagorean theorem:
r² = x² + y²
Where:
r - Hypotenusex, y - LegsAccording to the statement, we need to use the following relationships:
B = √(C² - A²)
a / A = b / B = c / C
If we know that A = 49, C = 90 and c = 12.7, then the lengths of missing sides are:
B = √(90² - 49²)
B = √5699 (approx. 75.5)
b = B × (c / C)
b = √5699 × (12.7 / 90)
b = 127√5699 / 900 (approx. 10.7)
a = A × (c / C)
a = 49 × (12.7 / 90)
a = 6233 / 900 (approx. 6.9)
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Find X then find angle NK
Using the two tangent exterior angle theorem:
x = 6
m(NK) = 153°
How to Apply the two tangent exterior angle theorem?According to the two tangent exterior angle theorem, when you draw two tangent lines from a point outside a circle, the angle formed between them is equal to half the difference between the measures of the arcs they intercept inside the circle.
Therefore, using the above theorem, we have:
7x + 6 = 1/2[(25x + 3) - (9x + 3)]
Solve for x:
2(7x + 6) = 25x + 3 - 9x - 3
14x + 12 = 16x
14x - 16x = -12
-2x = -12
x = -12/-2
x = 6
m(NK) = 25x + 3 = 25(6) + 3
m(NK) = 153°
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