The length of the garden which is in the shape of a rectangle with a perimeter of 18 meters and whose length is 3 meters more than twice the width, is 7 metres.
Let's name the width "w" and the length "l" of the rectangle.
We know from the problem description that the rectangle's perimeter is 18 metres, thus we can formulate an equation:
2l + 2w = 18
We also know that the length is 3 metres longer than the breadth, thus we can solve the following equation:
l = 2w + 3
We may plug the second equation into the first to remove the letter "l" and get an equation with only one variable:
2(2w + 3) + 2w = 18
When we simplify this equation, we get:
6w + 6 = 18
When we subtract 6 from both sides, we get:
6w = 12
When we divide both sides by 6, we get:
w = 2
We can use the second equation to get the length now that we know the width is 2 metres:
l = 2w + 3 = 2(2) + 3 = 7
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What is the area of the compound figure?
Answer:
42 mi²
Step-by-step explanation:
Break it up into 2 shapes, top and bottom, then add the areas together.
Area 1 (top rectangle) = 12 x 3 = 36
Area 2 (bottom rectangle) = 2 x 3 = 6
Total area = 36 + 6 = 42 mi²
Find a possible formula for the trigonometric function whose values are in the following table.
The formula possible formula for the trigonometric function whose values are in the following table is y = 6 x sin(π/2 * x) - 4.
What is a trigonometric function?Trigonometric functions are described as the periodic functions which denote the relationship between angle and sides of a right-angled triangle.
The formula for a trigonometric function is typically written as :
y = a sin (bx + c) + d
where a, b, c, and d are constants which tells us the amplitude, frequency, phase shift, and vertical shift of the function, respectively.
From the above table, the amplitude = 6,
the frequency is 2π/4 = π/2
the phase shift = 0, and
the vertical shift = -4.
Therefore, we can write the formula for the function as Y = 6 * sin(π/2 * x) - 4.
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Find an Angle Measure T ✓ The optimal tilt for Keenan's solar panelis between 58° and 60° to the horizontal. Has Keenan placed his solar panel at an optimal angle? SOLUTION COMMON ERROR 18 ft
Keenan has placed his solar panel at an optimal angle.
How determine if Keenan has placed his solar panel at an optimal angle?The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:
cos(C) = (a² + b² - c²) / 2ab
where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.
Check the attached image for labelling.
The angle we are trying to calculate is labelled C.
cos (C) = (20² + 18² - 19²) / (2*20*18)
cos (C) = 363/720
C = cos⁻¹(363/720)
C = 59.72°
Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.
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What percentage of K25 is 25t
The percentage K 25 that is 25 t, can be found to be 1 % .
How to find the percentage ?The relationship between K and t is such that 1 K has 100 t.
This means that K 25 in terms of t, would be:
= 25 x 100
= 2, 500 t
The percentage of K that is 25 t is therefore :
= 25 / 2, 500
= 1 / 100
= 0. 01
= 1 %
In conclusion, when given the values K 25 and 25 t, then 25 t would be 1 % of K 25.
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superior segway tours gives sightseeing tours around chicago, illinois. it charges a one-time fee of $45, plus $25 per hour. what is the slope of this situation?
If they charges a one-time fee of $45, plus $25 per hour, then the the slope of this situation is $25 per hour.
The situation described can be represented by the linear equation
Cost = $45 + $25 × hours
where "Cost" is the total cost of the tour and "hours" is the number of hours for which the tour is taken.
The slope of this equation represents the rate of change in the cost of the tour with respect to the number of hours.
In other words, it tells us how much the cost increases for each additional hour of the tour.
The slope of this equation is simply the coefficient of the "hours" variable, which is $25.
Therefore, the slope of this situation is $25 per hour.
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Answer:
$25 per hour.
Step-by-step explanation:
2x+2y=4;8x-2y=-4
Solve for linear equations by ELIMINATION. Show your work.
The solution to the system of given linear equations is x = 0 and y = 2.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
The system of equations is given in the question, as follows:
2x + 2y = 4 .....(i)
8x - 2y = -4 .....(ii)
To eliminate y, add the two equations together:
2x + 8x = 4 - 4
10x = 0
Solve for x:
x = 0
Now that we have x, we can substitute it back into one of the original equations to find y:
2x + 2y = 4
2(0) + 2y = 4
2y = 4
y = 4/2
y = 2
Thus, the solution is x = 0 and y = 2.
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How do I do this problem.
Answer:
1. 11π/6
2. 43π/18
3. -π/4
4. - 43π/18
5. 23π/6
6. 25π/18
Step-by-step explanation:
A full circle has a measure of 360° in degrees and 2π radians in radians.
Since a full circle has a measure of 2π radians, then half a circle has a measure of π radians, and a quarter circle has a measure of π/2 radians.
1. 2π - π/6 = 11π/6
2. 61π/36 - π/2 = 61π/36 - 18π/36 = 43π/18
3. 5π/4 - π = π/4; -π/4
4. -36π/18 - 7π/18 = -43π/18
5. 2π + π + 5π/6 = 23π/6
6. 36π/18 - 11π/18 = 25π/18
mr. tabor believes that less than 75% of the students at his school completed their math homework last night. the math teachers inspect the homework assignments from a random sample of 50 students at the school. what are the appropriate hypotheses for performing this significance test?
The null hypothesis statement is that the population is equal to the value mentioned in the claim:
[tex]H_{0} =P=75%=0.75[/tex]=[tex]\frac{75}{100}[/tex]=[tex]0.75[/tex].
[tex]H_{0} =P < 0.75[/tex]
The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis.
[tex]H_0} =P < 0.75[/tex]
A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.
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a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 420 gram setting. is there sufficient evidence at the 0.01 level that the bags are underfilled? based on a 37 bag sample, the manufacturer fails to reject the null hypothesis. what is the conclusion?
The conclusion is that the bag filling machine appears to be working correctly at this setting.
Based on the information provided, the manufacturer conducted a hypothesis test to determine if the bags are underfilled at the 420 gram setting. The null hypothesis (H0) is that the bags are not underfilled, while the alternative hypothesis (H1) is that the bags are underfilled.
Since the manufacturer failed to reject the null hypothesis at the 0.01 level of significance, this means that there is not enough evidence to support the claim that the bags are underfilled at the 420 gram setting. In other words, the bag filling machine appears to be working correctly at this setting.
It's important to note that the conclusion may change if the sample size or the level of significance is different. Additionally, other factors such as the accuracy of the measuring device used or the consistency of the banana chips themselves may also impact the results.
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5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar
If 5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar, We will be having 7 grams of sugar for one ounce of mango and 6 1/4 grams of sugar for one ounce of pineapple.
The problem states that we have 5 1/2 ounces of mango with 17 1/2 grams of sugar, and 4 ounces of pineapple with 25 grams of sugar. We are asked to determine the grams of sugar per ounce for each type of food. To determine the grams of sugar per ounce for each type of food, we can use the following calculations:
For mango: 5 1/2 ounces is equivalent to 11/2 + 1/2 = 2 ounces + 1 ounce/2, so we have 17 1/2 grams of sugar in 2 1/2 ounces of mango. To find the grams of sugar per ounce, we can divide 17 1/2 by 2 1/2, which gives us 7 grams of sugar per ounce of mango.
For pineapple: 4 ounces of pineapple has 25 grams of sugar. To find the grams of sugar per ounce, we can divide 25 by 4, which gives us 6 1/4 grams of sugar per ounce of pineapple.
Therefore, the grams of sugar per ounce for mango and pineapple are 7 and 6 1/4, respectively.
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Complete question is:
5 1/2 ounce of mango has 17 1/2 grams of sugar and 4 ounces of pineapple has 25 grams of sugar. Determine the grams of sugar for ounce for each type of food.
Which of the following is equal to the square root of the cube root of 5?
Group of answer choices
5 to the power of one third
5 to the power of one sixth
5 to the power of two thirds
5 to the power of three halves
5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
What is the definition of square root?
The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.
If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.
Now,
Given that square root of the cube root of 5 i.e. √∛5=?
=√5¹÷³
=5¹/²*¹/³
=5¹/⁶
hence,
5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.
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Is y=5 and x=-1 parallel
Answer:
y=5 and x=-1 are parallel
Step-by-step explanation:
Let's do a quick review on some things:
Parallel lines are the lines that never intersect and perpendicular lines are the lines that intersect at 90°.
Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.
So, this answers to your question that it's parallel!
Hopefully this helps :)
refer to the previous two questions: what is the probability that only one of the two failure modes will occur over the life of the building? (answer correct to 3 decimal places) hint: start by thinking components of the event failure by only one mode (what options does that imply?)
Probability that only one of the two failure modes will occur over the life of the building is 0.11
The probability for failure of building
P (Failure) = P(C U E)
= P(C) - P(E) - P(CUE) - P(C|E)P(E)
Substitute 0.05 for P(C) 0.1 for P(E) and 0.2 for PC/E) in equation to find the probability for failure.
P(failure) = P(CUE)
= 0.05 +0.1 -0.2 x 0.1
= 0.13
Probability that only one of the two failure modes will occur over the life of the building
P(CE U EC) = P(ČE) + P(EC)
= P(C U E) - P(EC)]
= P(CUE) - P(C|C)P(E)
Substitute 0.13 for P(CUE) 0.1 for P(E) and 0.2 for P(CIE) in equation (3) to find P(CE UĒC).
P(CE U EC) - 0.13 - (0.2 x 0.1)
= 0.11
Hence,
Probability that only one of two failure modes will occur over the life of the building is 0.11.
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two cards are selected from a standard deck of 52 playing cards. the first card is not replaced before the second card is selected. find the probability of selecting a black card and then selecting a red card.
The probability of selecting a black card first and a red card second from a standard deck of 52 playing cards without replacement is 13/51.
The probability of selecting a black card on the first draw is 26/52, or 1/2, since there are 26 black cards in a standard deck of 52 playing cards.
After the first card is drawn, there are 51 cards remaining, of which 26 are red. Therefore, the probability of selecting a red card on the second draw, given that a black card was selected on the first draw, is 26/51.
To find the probability of both events happening (selecting a black card followed by a red card), we multiply the probabilities of each event:
P(black card first, red card second) = P(black card first) × P(red card second | black card first)
P(black card first, red card second) = (1/2) × (26/51)
P(black card first, red card second) = 13/51
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3=2x+y
4x+6=10y
Find what is x and what is y
Answer:
x=1 , y=1
Step-by-step explanation:
2x+y=3 - - (1)
4x+6=10y
=> 4x-10y=-6 - - (2)
Multiply eq (1) by 2, and we get ;
4x+2y=6 - -(3)
Now subtract eq (3) by eg (2)
4x+2y=6
-4x+10y=+6
12y=12
y=1
Sub value of y in eq (1)
2x+1=3
2x=2
x=1
Every week at the Cougar Scouts meeting, Jamal is in charge of the craft activity. This week, he decides to make pinecone bird feeders. At the meeting, Jamal divides a bag of birdseed evenly among 12 Cougar Scouts, and each scout gets 1/2 of a cup of birdseed. Use an equation to find the amount of birdseed in the bag.
To write a fraction, use a slash (/) to separate the numerator and denominator.
The mean of x, y, and z is 55. If x+y=107 then what does z equal?
Answer:
The value of z is 58
Step-by-step explanation:
The mean is the average of a set of numbers. Mean = (sum of the numbers)/(the number of numbers).
We are told that the mean of x+y+z is = 55.
We can wriote this as:
55 = (x+y+z)/3
We learn that x+y = 107. So lets enter that number for x + y:
55 = (x+y+z)/3
55 = ((x+y)+z)/3
55 = ((107)+z)/3 [Substitution]
55 = (107+z)/3
165 = 107+z [Multiply both sides by 3]
z = 58 [Simplify]
CHECK:
Is the mean of x, y, and z 55?
55 = (x+y+z)/3 ?
55 = ((107)+z)/3 ? [Since we know x+y = 107]
55 = ((107)+58)/3 ? [Since z=58]
55 = (165)/3) ?
55 = 55 YES The value of z is 58
Look at the table of values. What is the vertex of the graph? How do you know?
The vertex of the given graph is (5, 0)
What is vertex:A vertex is a point on a polygon where two rays or line segments meet, and the sides or edges of the object come together. Vertex is the plural form of vertices.
A straight line that can be extended endlessly is known as a ray. An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle.
Thus, we can state that a vertex is formed when two line segments or rays intersect.
Here we have a graph
The equation of the graph is y = |x - 5| + 1
As we can see that two lines are intersected at a point (5, 0)
Therefore,
The vertex of the given graph is (5, 0)
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What is 36 + 45 rewritten as the product of a whole number and the sum of two whole numbers with no common factor
By using the distributive property the sum "36 + 45" can be expressed as product and sum of 2 numbers as 9 × (4 + 5) .
The Distributive Property states that a × (b + c) = a×b + a×c, where a, b, and c are any real numbers.
Using this property, we can rewrite the sum 36 + 45 as:
⇒ 36 + 45 = 9 × 4 + 9 × 5
Factoring out the common factor of 9,
we get ;
⇒ 36 + 45 = 9 × (4 + 5) ;
Therefore, the sum 36 + 45 as the product of a whole number (9) and a sum of two whole numbers (4 and 5) is 9×(4 + 5) .
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The given question is incomplete , the complete question is
What is 36+45 by using the distributive property to rewrite the sum as the product of a whole number other than 1 and a sum of two whole numbers ?
A quadrilateral has two angles that measure 100° and 90°. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
The measures of angles C and D are 70° and 100°, respectively.
Understanding angles is a fundamental concept in geometry. A quadrilateral is a polygon with four sides, and its angles are essential to determining its properties.
Let's start by labeling the angles in the quadrilateral. We know that two angles measure 100° and 90°, so let's label them as A and B, respectively. The other two angles, which we are trying to find, can be labeled as C and D.
Now, we are given that the ratio of angles C and D is 7:10. This means that we can write the following equation:
C/D = 7/10
We can use this equation to solve for one of the angles. Let's choose angle C. We can rewrite the equation as:
C = (7/10)D
We also know that the sum of the angles in a quadrilateral is 360°. Therefore, we can write another equation:
A + B + C + D = 360°
We can substitute the values we know into this equation and solve for angle D:
100° + 90° + (7/10)D + D = 360°
Simplifying the equation:
(17/10)D = 170°
D = 100°
Now that we know the value of angle D, we can use the equation we derived earlier to find the value of angle C:
C = (7/10)D = (7/10) x 100° = 70°
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A circle has a radius of 3 inches. What is the circumference of the circle? (Use 3.14
for pi.)
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Answer: 18.84
Step-by-step explanation:
because the radius is 3, the diameter is 6. And the circumference is C=pi(d).In this case, C=3.14(6), and 3.14*6=18.84
Use the following expression to answer the following questions.
I
t+0.24t
The decimal in the expression represents what value as a percent? (No % sign.)
Is the expression representing an increase or a decrease? Percent Increa: V
Create the simplified version of the expression.
The percentage increase is given by the equation A = t + 0.24t = 1.24t
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage increase be represented as A
Now , the equation will be
The initial quantity be represented as t
Now , the increased quantity be represented as p = 24 %
So , the increased quantity = 24 % x initial quantity
Substituting the values in the equation , we get
The increased quantity = ( 24/100)t
The increased quantity = 0.24t
So , the final quantity = initial quantity + increased quantity
On simplifying the equation , we get
The final quantity = t + 0.24t
The final quantity = 1.24t
Hence , the equation is A = 1.24t
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Melanie is raising money for a school trip by selling candy bars and bags of chips. The price of each candy bar is $1.50 and the price of each bag of chips is $1.25. Yesterday Melanie made $33.25 and sold 13 more candy bars than bags of chips. Determine the number of candy bars sold and the number of bags of chips sold.
Both the quantity of candy bars and bags of chips sold are Melanie sold five bags of chips and eighteen candy bars (5 + 13).
What does sold mean?A product that has been sold has been exchanged for cash. You'll notice a "Sold" sign appear in the front yard of the house across the street whenever new neighbours purchase it.
Is it sold or is it sold?In addition to being a noun, the verb sell has three different tenses: simple present, simple past, and past participle. I'll sell my current vehicle and purchase a new one. She is distributing water bottles at the football game. My old college textbooks were all sold on the internet yesterday.
Let x be the number of bags of chips sold, then the number of candy bars sold would be x + 13.
The total revenue from the sales of the bags of chips would be $1.25 * x and the total revenue from the sales of the candy bars would be $1.50 * (x + 13).
Since the total revenue was $33.25, we can set up an equation:
$1.25x + $1.50(x + 13) = $33.25
Expanding and simplifying the right side:
$1.25x + $1.50x + $19.50 = $33.25
Combining like terms:
$2.75x + $19.50 = $33.25
Subtracting $19.50 from both sides:
$2.75x = $33.25 - $19.50 = $13.75
Dividing both sides by $2.75:
x = $13.75 / $2.75 = 5
So Melanie sold 5 bags of chips and 5 + 13 = 18 candy bars.
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What is | −34 |?
????
Answer:
34
Step-by-step explanation:
The absolute value of a real number [tex]a[/tex] is [tex]a[/tex] when [tex]a[/tex] ≥ 0, or −[tex]a[/tex] when [tex]a[/tex] < 0. The absolute value of −34 is 34.
Hope it helps and have a great day! =D
The class figured out that if the percent increase is 99% from the beginning of the year, the class will have enough money for every student to go on the field trip. How much money will the class need to raise for every student to go
Answer:
Step-by-step explanation:Class Trip Fund Calculation
The class figured out that if the percent increase is 99% from the beginning of the year, the class will have enough money for every student to go on the field trip. How much money will the class need to raise for every student to go
To calculate the amount of money that the class needs to raise, you can use the formula for calculating the amount after a percent increase:
amount = original amount + (original amount * percent increase / 100)
Let's assume that the original amount is x. After a 99% increase, the new amount will be:
x + (x * 99 / 100) = x * 199 / 100
So, to find the original amount, you can set up an equation:
x * 199 / 100 = amount needed for the field trip
And then solve for x:
x = amount needed for the field trip * 100 / 199
So, the class needs to raise an amount equal to the amount needed for the field trip * 100 / 199 to have enough money for every student to go on the field trip.
Find the missing length the triangles are similar
Answer:
[tex]49[/tex]
Step-by-step explanation:
[tex]\frac{US}{UD}=\frac{UT}{UC} \implies US=\frac{(56)(14)}{16}=49[/tex]
The following percentages were obtained over many years of observation by the U. S. Weather Bureau. All data listed are for the month of December.
Location
Long-Term Mean % of Clear Days in Dec.
Juneau, Alaska
18%
Seattle, Washington
24%
Hilo, Hawaii
36%
Las Vegas, Nevada
75%
Phoenix, Arizona
77%
In the locations listed, the month of December is a relatively stable month with respect to weather. Since weather patterns in these locations from one day to the next are more or less the same, it is reasonable to use a binomial probability model.
Let r be the number of clear days in December. Since December has 31 days, 0≤r≤31. Nm4u0IVE95dhb8ATPw0weRwYAkAAAAASUVORK5CY P(r)yEe62CYUPB7MJz5G6C+JLsVriPljwPUUJXmslZLy is the binomial probability for each of the listed locations when r=0, 1, 2, … , 31f+RvZvj8MDoTWn4AAAAASUVORK5CYII=. Include your formula setup or calculator comments to answer the following questions.
(1 pt) Find the probability that Juneau will have at most 8 clear days in December.
(1 pt) Find the probability the Hilo will have at least 14 clear days in December.
(1 pt) Find the probability that Phoenix will have 20 or more clear days in December.
(1 pt) Find the probability that Las Vegas will have no more than 18 clear days in December.
(2 pts) Find the probability that Seattle will have from 5 to 10 (including 5 and 10) clear days in December
The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.
1. P(r≤8) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)= 0.7608
2. P(r≥14) = 1 - P(r≤13) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13))= 0.7367
3. P(r≥20) = 1 - P(r≤19) = 1 - (P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)+ P(r=19))= 0.4672
4. P(r≤18) = P(r=0) + P(r=1) + P(r=2)+ P(r=3)+ P(r=4)+ P(r=5)+ P(r=6)+ P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)+ P(r=11)+ P(r=12)+ P(r=13)+ P(r=14)+ P(r=15)+ P(r=16)+ P(r=17)+ P(r=18)= 0.9590
5. P(5≤r≤10) = P(r=5) + P(r=6) + P(r=7)+ P(r=8)+ P(r=9)+ P(r=10)= 0.5385
The probability of having at most 8 clear days in Juneau, 14 or more in Hilo, 20 or more in Phoenix, 18 or less in Las Vegas, and between 5 and 10 in Seattle is 0.7608, 0.7367, 0.4672, 0.9590, and 0.5385, respectively.
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I NEED ANSWER ASAP IM GIVING A LOT OF POINTS
Answer:
The answer is 26
Step-by-step explanation:
The system is easy16-6=10,15-5=1010+10+18=38For the missing number.16-15=1,8-2=61+6+19=26Need help with this for school
Answer:
135
Step-by-step explanation:
The max value is where the far right point of the "whisker" is.
Compare 3/10 and 25/100 which one is greater
Answer:
The answer to your question is 3/10
How do you compare fractions?
First lets find similar fractions
2.5/10 = 25/100 We know that.
Since 3/10 is bigger that 2.5/10 by .5 it would basically conclude that 3/10 is greater/bigger the the fraction 25/100.
