The null hypothesis, denoted by H0, represents the status quo or the default assumption. In this case, the null hypothesis is that the average water consumption in Montana residences is 125 gallons per week.
The alternative hypothesis, denoted by Ha, is the hypothesis that the researcher is trying to prove. In this case, the alternative hypothesis is that the average water consumption in Montana residences is not equal to 125 gallons per week.
So, the null and alternative hypotheses for this problem are:
H0: μ = 125 (where μ is the population mean water consumption in Montana residences)
Ha: μ ≠ 125 (where μ is the population mean water consumption in Montana residences)
Note that the alternative hypothesis is a two-tailed hypothesis since we are testing whether the population mean is not equal to 125, which could mean it is either greater or less than 125.
F
G
9x-7
E
17x-2
Solve for x
The solution for x in the circle is x = 12
How to solve for the value of x in the circle?Since the measure of angle EFG is m∠EFG = 9x-7 and the measure of arc GE is 17x-2
We can determine the value of x using the inscribed angle theorem.
Thus, we have:
m∠EFG = 1/2 (arc GE)
9x-7 = 1/2 * (17x-2)
2(9x-7) = 17x - 2
18x - 14 = 17x - 2
18x - 17x = -2 + 14
x = 12
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What is the area and perimeter of semicircle?
Area of semicircle is (πr²)/2 and perimeter is (πr) + 2r
The area and perimeter of a semicircle can be calculated using the formulas for the area and circumference of a full circle, and then dividing by 2.
The formula for the area of a full circle is A = πr², where r is the radius of the circle. So the area of a semicircle would be A = (πr²)/2.
The formula for the circumference of a full circle is C = 2πr, where r is the radius of the circle. The perimeter of a semicircle would be half of the circumference, plus the diameter (which is 2r). So the perimeter of a semicircle would be P = (πr) + 2r.
So, to find the area and perimeter of a semicircle, you would need to know the radius of the semicircle, and then plug it into the formulas above.
For example, if the radius of the semicircle is 4, the area would be A = (π(4²))/2 = 8π, and the perimeter would be P = (π(4)) + (2(4)) = 4π + 8.
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If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4 . If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Find the fraction.
The fraction is given as follows:
8.3/10.3.
How to obtain the fraction?The fraction is modeled as follows:
x/y.
In which:
x is the numerator.y is the denominator.From the features of the problem, a system of equations is built to identify the variables.
If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4, hence the first equation is of:
4x/(y - 2) = 4.
Hence:
4x = 4(y - 2)
4x = 4y - 8
x = y - 2.
If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4, hence the second equation is of:
(x + 15)/(2y - 2) = 5/4.
We know that x = y - 2, hence the value of y is obtained as follows:
(y + 13)/(2y - 2) = 5/4.
5(2y - 2) = 4(y + 13)
10y - 10 = 4y + 52
6y = 62
y = 62/6
y = 10.3.
Then the value of x is of:
x = y - 2
x = 10.3 - 2
x = 8.3.
Hence the fraction is:
8.3/10.3.
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Question 15(Multiple Choice Worth 4 points)
(02.04 MC)
What is the equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8,-4)?
Oy=-x-2
Oy=-x+7
Oy=4x-36
Oy = 4x + 24
An equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, -4) is y = -x/4 - 2
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
4 × m₂ = -1
m₂ = -1/4
At point (8, -4), an equation of the line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-4) = -1/4(x - 8)
y + 4 = -1/4(x - 8)
y = -x/4 + 2 - 4
y = -x/4 - 2
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I will give you brainy
A landscaper needs 3 1/5 pounds of fertilizer. He has 1 3/10 pounds in his truck, and another 1/5 pound at his shop.
How many more pounds of fertilizer does the landscaper need?
Enter your answer as a mixed number in simplest form by filling in the boxes.
help pleases
Answer:
1
Step-by-step explanation:
12
find the area of a sector with a central angle of 200 and a diameter of 7.5 cm round to the nearest tenth
Answer:
need points srry
Step-by-step explanation:
does anyone know how to do this?
Step-by-step explanation:
Is there more to this question? I feel like the 2021 federal income tax bracket is missing
PLEASE HELP WILL GIVE BRAINLIEST
help with this proof please image attached
Answer:
Step-by-step explanation:
If AB║DC,
∴∡BAC=∡ACD(ALTERNATE aNGLES)
AB=DC
AC=AC (COMMON SIDE)
∡BAC=∡ACD (PROVED)
∴ ΔABC≡ΔACD(S.A.S)
∴EF=FG
Select all of the ways to describe the number 182.
Answer choices
A rational number
B integer
C whole number
D none of these are correct
Answer:
A , B and C
Step-by-step explanation:
182 is a rational number as it can be written in p/q form. (182/1)
182 is a positive integer. {Integers: ........ -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 .......}
182 is a whole number. {0, 1 , 2 , 3 ,...............}
what are the minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm
The minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.
What is triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points. The three sides and three angles of a triangle are interconnected by various geometrical principles and formulas, such as the Pythagorean theorem, trigonometric ratios, and the Law of Cosines. Triangles are commonly classified based on their side lengths and angles, including equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles are also used in various real-life applications, such as in architecture, engineering, and physics.
According to given information :To complete a triangle with side lengths 18 cm and 21 cm, the length of the third side must be such that it satisfies the triangle inequality. The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.
Let x be the length of the third side. Then we have:
18 + 21 > x
18 + x > 21
21 + x > 18
Simplifying each inequality, we get:
x < 39
x > 3
x > -3 (since length cannot be negative)
The minimum value of x is 3 cm (when the two sides form a degenerate triangle), and the maximum value of x is 39 cm (when the three sides form an equilateral triangle). Therefore, the minimum and maximum side lengths to complete a triangle with two side lengths of 18 cm and 21 cm are 3 cm and 39 cm, respectively.
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Lynn is making a snack. The recipes call for 38
cup of water for oats and 14
cup of water for dried fruit. She only has 1 cup of water. Does she have enough to make her snack? Explain.
Answer:
The last choice
Step-by-step explanation:
Since 3/8 is smaller than 1/2(=4/8) and 1/4 is also smaller than 1/2(=2/4), she has enough water to make her snacks.
I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!
Need answer now! Please and thank you !!
Answer: A sorry if i got it wrong
Step-by-step explanation:
Find the length of BC.
Give your answer to 1 decimal place.
the length of BC is 11.9 cm.
What is right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given a right triangle ABC with hypotenuse AC and the foot angle of 58-degree.
Using the sine ratio in the right triangle
sin58° = (Opposite side)/(hypotenuse)
In our case,
opposite side = height
opposite side = BC
hypotenuse = AC
hypotenuse = 14(given)
So,
Multiply both sides by 14
14 × sin58° = BC, thus
BC ≈ 11.9 cm
Therefore, the height of the given right angle triangle will be 11.9 cm(Approx.).
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Complete question:
Scenario: It cost $5 to Roller Skate for 2 hours at Empire Roller Skating ring.
Identify the cost per hour for this recreational activity in the scenario
(Unit Rate)
The cost per hour for this recreational activity in the scenario which is also the unit rate is $2.5 per hour.
What is the cost per hour for the recreational activity?Number of hours= 2 hours
Total cost to roller skate = $5
Cost per hour of recreational activity= Total cost to roller skate / Number of hours
= $5 / 2 hours
= $2.5 per hour
In conclusion, it costs $2.5 per hour to roller skate.
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Question 3 3.1.1. Express the following as single trigonometry ratio: 3.1.1. Cos2x · Cos3x - Sinax. Sin3x 2 B12. Sinzx Cosx+Cosex Sinx 3.2. Determine the value of the following without using a calcula 3.2.1. Sın 85° Cos25°- Cos 85°. Sin 25° 322 Cos 160°. Cos10° + Sin160°. Sin 10° 44
Using trigonometric identity, the value of the expressions are (Cosx + Cos5x)/2 + Sin3x.Cosx, √3/2, √3/2 and -√3/2
What is the expression of the trigonometric identityTo solve this problem, we need to apply trigonometric identity;
1.
Cos2x · Cos3x - Sinax. Sin3x:
Using the identity Cos(A - B) = CosA.CosB + SinA.SinB, we can write:
Cos2x · Cos3x = (Cos(2x - 3x) + Cos(2x + 3x))/2 = (Cos(-x) + Cos(5x))/2 = (Cosx + Cos5x)/2
So the expression becomes:
(Cosx + Cos5x)/2 - Sinax. Sin3x
Using the identity Sin(A - B) = SinA.CosB - CosA.SinB, we can write:
Sinax. Sin3x = (Sin(ax - 3x) - Sin(ax + 3x))/2 = (Sin(-2x) - Sin(4x))/2 = (-Sin2x - Sin4x)/2
So the expression becomes:
(Cosx + Cos5x)/2 + (Sin2x + Sin4x)/2
Using the identity SinA + SinB = 2.Sin((A+B)/2).Cos((A-B)/2), we get:
(Sin2x + Sin4x)/2 = Sin3x.Cosx
Therefore, the expression simplifies to:
(Cosx + Cos5x)/2 + Sin3x.Cosx
2.
Sinzx Cosx+Cosex Sinx:
Using the identity Sin(A + B) = SinA.CosB + CosA.SinB, we can write:
Sinzx Cosx+Cosex Sinx = Sin(x + z)
So the expression is equivalent to Sin(x + z).
3.
Sın 85° Cos25°- Cos 85°. Sin 25°:
We can use the identity Sin(A - B) = SinA.CosB - CosA.SinB:
Sin 85° Cos25°- Cos 85°. Sin 25° = Sin(85° - 25°) = Sin60° = √3/2
4.
Cos 160°. Cos10° + Sin160°. Sin10°:
We can use the identity Cos(A - B) = CosA.CosB + SinA.SinB:
Cos 160°. Cos10° + Sin160°. Sin10° = Cos(160° - 10°) = Cos150° = -√3/2
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The image on a movie poster was shrunk to make the DVD cover art for the movie, so that the cover art is a scale image of the poster. The poster is 72 inches wide, and the DVD cover art is 6 inches wide. If the diagonal of the poster is 8 feet, what is the diagonal of the DVD cover art?
A.
8 inches
B.
24 inches
C.
7 inches
D.
0.67 inch
The diagonal of the DVD cover art has a length of 8 inches. (Correct choice: A)
How to use scales to find the length of the diagonal of the DVD cover art
In this question we need to estimate the length of the diagonal of the DVD cover art, this can be used by means of scale factor relative to the width of the movie cover. Scales are an useful resource to represent systems at affordable dimensions. By assuming that both DVD cover art and movie cover have similar geometries, we can estimate the diagonal of the DVD cover art by proportion formula:
6 in / 72 in = x / [(8 ft) · (12 in / ft)]
x = (6 in / 72 in) × 96 in
x = 8 in
The length of the diagonal of the DVD cover art is equal to 8 inches.
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Evaluate. x =2 and y=-1
Can someone help please,I also need explanation of not much to ask
Answer:
= 16.
Step-by-step explanation:
x= 2
y = -1
[tex] {(2xy)}^{2} \\ = {(2(2)( - 1)) \\ }^{2} \\ = {(2( - 2)) \\ }^{2} \\ = {( - 4)}^{2} \\ = - 4 \times - 4 \\ = 16[/tex]
How many times is 7 a factor in 2023!
Answer:
The Prime Factors and Pair Factors of 2023 are 7 × 17 and (1, 2023), (7, 289), (17, 119) respectively.
Answer:
To determine how many times 7 is a factor in 2023:
1. Divide 2023 by 7 to obtain the quotient: 2023/7 = 288.571.
2. If the result of the division is a whole number, 7 is a factor in 2023.
3. Round down 288.571 to obtain the integer 288.
4. Since the result of the division is a whole number, 7 is a factor in 2023 and occurs 1 time.
types as many equations
basically draw 1 linear line with domain constraints for the first two
y = 1/2x + 6 {7<x < 13}
y = 1/2x + 3 {x<7}
the values might have to be tweaked a little as the stars are not exactly on point
If one object has twice as much mass as another object it also has twice as much.
If one object has twice as much mass as another object it also has twice as much Inertia.
Let the mass of object A= m₁
mass of object B = m₂
Given that m₁ = 2m₂
Speed, velocity and acceleration are subject to motion of the object. Given the insufficiency of information in the question, nothing can be said about these.
This is basically Newton's first law of motion, this law states that, every object continues in a state of rest of uniform motion in a straight line, unless acted upon by an external force
On the other hand, inertia is directly dependent on the mass. Hence, inertia of object A would be twice the inertia of object B.
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.please help!!!!!!!!
Answer:
226.19 cubic units
Step-by-step explanation:
radius = r = 6 units
height = h = 6 units.
To find the volume of resulting solid, subtract the volume of cone from the volume of hemisphere.
Volume of the resulting solid = Volume of hemisphere - volume of cone
[tex]\sf \bf = \dfrac{2}{3}\pi r^3 - \dfrac{1}{3}\pi r^2h\\\\\\=\dfrac{2}{3}*3.14*6*6*6 - \dfrac{1}{3}*3.14*6*6*6\\\\\\=(3.14*6*6*6)(\dfrac{2}{3}-\dfrac{1}{3})\\\\=3.14*6*6*6**\dfrac{1}{3}\\\\=3.14*6*6*2\\\\=226.19 \ cubic \ units[/tex]
solve the system of linear equations by elimination
3x+4y=-1
-2x-5y=10
Answer:
x = 5
y = -4
Step-by-step explanation:
Solving system of linear equations:3x + 4y = -1 -----------(I)
-2x - 5y = 10 -----(II)
Multiply equation (I) by 2 and equation (II) by 3 and then add. Doing so, x will be eliminated, and we can find the value of 'y'.
(I) * 2 6x + 8y = -2
(II)* 3 -6x - 15y = 30 {Now add}
-7y = 28
Divide both sides by (-7),
y = 28 ÷ (-7)
[tex]\boxed{y=(-4)}[/tex]
Plugin y = (-4) in equation (I),
3x + 4*(-4) = -1
3x - 16 = -1
3x = -1 +16
3x = 15
x = 15÷3
[tex]\boxed{x=5}[/tex]
How do I calculate my grade calculator?
Formula used to calculate the grades to a student is as follows:
F=G−((1−w)×C))/w.
You may determine the grade you need on the final exam to get your desired course grade if you know your present grade and the final test's weight.
The explanation for the given formula, F = Final exam grade
G = Grade you want for the class
w = Weight of the final exam, divided by 100 (put weight in decimal form vs. percentage form)
C = Your current grade.
Being able to keep track of your class grades is a really valuable ability. You may keep track of your progress and see whether you need to work more to achieve the grade you want. In order to figure out how much you need to raise your grade with a point system. Compare that number against the point count for the work you have not yet done. Thus this is the way to calculate grades.
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A chef uses a bowl shaped like the one below to prepare her avocado lime sauce. Due to the amount of mixing involved in this recipe she does not want to fill the bowl up entirely to the top. She estimates she can only fill the bowl up to about 2/3 its capacity. What is the volume of contents the chef will be able to fill the bowl with using her estimation?
Answer: DON'T COPY AND PASTE!! a-lot of people say they get a plagiarism charge so try to switch or add more words to this but i hope it helps!!!
Step-by-step explanation:
Claim - The volume of the bowl is 715.17
evidence - The hemisphere has a radius of 8
- so its volume is 2/3πr³ r = radius
= 2/3 × π × (8)³
she can fill = 2/3 × 2/3 × 22/7 × (8)³ cm³
= 715.17cm³
reasoning - Therefore according to my calculations The volume will be 715.17 cm³
a notebook is 8 inches tall and 10 inches wide what is its area?
Answer:
i think 18
Step-by-step explanation:
In 2010, the population of a city was 88,000. From 2010 to 2015, the population grew by 4%. From 2015 to 2020, it fell by 3%. To the nearest 100 people, what was the population in 2020?
The population in 2020 is 2,240,700
What is population?A population is the set of people concentrated in a particular area.
Given that, in 2010, the population of a city was 88,000, from 2010 to 2015, the population grew by 4%. From 2015 to 2020, it fell by 3%. We need to determine the population in 2020,
For population growing we will multiply the population is 104 and for population reducing we will multiply by 97,
Therefore, the population in 2020 =
88000 × 5(104/100) × 5(97/100)
= 88000 × 5.25 × 4.85
= 2,240,700
Hence, the population in 2020 is 2,240,700
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7. The ratio of dahlias to sunflowers is the same in all of the
flower arrangements at a banquet.
A. MTR Use Structure Complete the double number line to
show the ratios of dahlias to sunflowers in all the flower
arrangements at the banquet.
12
Dahlias 0
4
Sunflowers 0
8
16
6
a
15 18
B. How many dahlias will there be when there are 33 sunflowers?
C. What is the ratio of dahlias to all flowers when there are 21 total
flowers?
D. What is the ratio of sunflowers to all flowers in a bouquet with
70 total flowers?
20 24
12
21
32
8 dahlias
24
6 sunflo
7A) The completion of the number line, based on the ratio of Dahlias to Sunflowers, is as follows:
Dahilas 0 4 8 12 16 10 24 28 32
Sunflowers 0 3 6 9 12 15 18 21 24
7B) When there are 33 sunflowers, there will be 44 Dahlias.
7C) The ratio of Dahlias to all flowers when there are 21 total flowers is 0.57:1 or 12:21.
7D) The ratio of Sunflowers to all flowers in a bouquet with 70 total flowers is 0.43:1 or 3:7.
What is the ratio?The ratio is the relative size of one value compared to another.
The ratio is determined as the quotient or average of two relative values.
The number of Dahlias = 8
The number of Sunflowers = 6
Ratio of Dahlias to Sunflowers = 1.33:1 (8:6)
Ratio of Sunflowers to Dahlias = 0.75: 1 (6:8)
The sum of ratios = 14 (8 + 6)
B) When there are 33 sunflowers, there will be 44 Dahlias (33/0.75).
C) The ratio of Dahlias to all flowers:
The total flowers = 21
Dahlias = 12 (21 x 8/14)
The Ratio of Dahlias to all flowers = 12:21 = 0.57:1
The ratio of dahlias to Sunflowers = 12:9
D) The ratio of Sunflowers to all flowers:
The total flowers = 70
Sunflowers = 30 (70 x 6/14)
The ratio of Sunflowers to all flowers = 30:70 = 0.43:1
Ratio of sunflowers to dahlias = 30:40 = 3:4
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Ryan wants to take out a $520,000 loan with an APR of 4.15% for 20 years. He purchased a discount point for 1% of his principal that will decrease his APR by 0.125%. If Ryan purchases 3 points, after how many months will he break even?
Answer:
It will take Ryan 59.6 years to break even on his purchase of 3 discount points (1% each) for a $520,000 loan with an APR of 4.15%. This break-even point was calculated by finding the difference in monthly payments between the loan with and without the discount points, and dividing the cost of the points by that difference.
Priovde the missing reasons for the proof
The missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ DBE by AA rule.
What are vertically opposite angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other. These are sometimes called vertical angles.
Given that, ∠ C ≅ ∠ E, and we need to find a reason to prove Δ ABC ~ Δ DBE,
As we know that, to prove two triangles similar we can show two corresponding angles congruent in them, then they will be similar by AA rule,
Here, we already have, ∠ C ≅ ∠ E, we need one more,
If we see the figure, we get ∠ ABC and ∠ DBE are vertically opposite angles
We know that, Vertically opposite angles are equal to each other.
Therefore, ∠ ABC ≅ ∠ DBE
Hence, the missing reason is ∠ ABC ≅ ∠ DBE by vertically opposite angles postulate and Δ ABC ~ Δ DBE by AA rule.
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Three values of x are in the table. What are the corresponding values of y so that each ordered pair is a solution of the equation y = 0.2x – 2?
x y
The corresponding values of y so that each ordered pair is a solution of the equation y = 0.2x – 2 is,
Input (x) -6 -1 1
Output (y) -3.2 -2.2 -1.8
What is the function rule?Function rule is the rule of writing the relationship between the two variables, one is dependent and another is independent.
The table given in the problem is;
Input (x) -6 -1 1
Output (y)
We have given the equation as;
y = 0.2x – 2
Complete the table using the above function rule;
At (x) equal to -6,
y = 0.2x – 2
y = 0.2(-6) – 2
y = -3.2
At (x) equal to -1,
y = 0.2x – 2
y = 0.2(-1) – 2
y = -2.2
At (x) equal to 1,
y = 0.2x – 2
y = 0.2(1) – 2
y = -1.8
Hence,
Input (x) -6 -1 1
Output (y) -3.2 -2.2 -1.8
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Answer:
Step-by-step explanation:
Input (x) -6 -1 1 Output (y) -3.2 -2.2 -1.8