Step-by-step explanation:
284.8 = 282.2 ( b)^1 1 is the number of years....looking for 'b'
284.8 / 282.2 = b = ~ 1.009
P(t) = 282.2 ( 1.009)^t where P(t) is in millions and :
The variable t represents the number of years since July of 2000. Round your value of b to the nearest thousandth.
R
x
PR 96 cm
PQ48 cm
What is the value of x ? Enter the answer in the box.
degrees
The value of x is 30 degrees.
Describe Right Angled Triangle?A right-angled triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of the two sides of the triangle that are perpendicular to each other, which are called the legs or the adjacent and opposite sides. The side opposite the right angle is called the hypotenuse, and it is always the longest side in the triangle. The other two sides are usually labeled as a and b, and are called the legs or the adjacent and opposite sides depending on which angle is being considered. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is one of the fundamental properties of right-angled triangles. Right-angled triangles have numerous practical applications in geometry, trigonometry, physics, and engineering.
We can use the trigonometric ratio of sine to find the angle x.
sin(x) = opposite/hypotenuse = PQ/PR = 48/96 = 1/2
Taking the inverse sine of both sides, we get:
x = sin^(-1)(1/2)
Using a calculator, we get:
x ≈ 30 degrees
Therefore, the value of x is 30 degrees.
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A standardized test is given to a sixth grade class and a seventh grade class. The superintendent believes that the variance in performance from the sixth grade class is greater than the variance in performance from the seventh grade class. The sample variance of a sample of 19 test scores from the sixth grade class is 34. 66. The sample variance of a sample of 18 test scores from the seventh grade class is 6. 3. Test the claim using a 0. 1 level of significance. Let σ21 represent the population variance for sixth grade class.
Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer(s) to four decimal places.
Please do all steps
The answer is 4.4753, i.e. the critical value of the statistic upto four decimal places.
Step 1 of 5: State the null and alternative hypotheses.Null hypothesis (H0): σ21 = σ22
Alternative hypothesis (H1): σ21 > σ22
Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma.Round your answer(s) to four decimal places.
Critical value = 4.4753
Step 3 of 5 : Calculate the test statistic:Test statistic = 34.66/6.3 = 5.5
Step 4 of 5 : Make a decision:The test statistic (5.5) is greater than the critical value (4.4753), so we reject the null hypothesis and accept the alternative hypothesis.
Step 5 of 5 : State a conclusion:We conclude that the variance in performance from the sixth grade class is greater than the variance in performance from the seventh grade class at a 0.1 level of significance.
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Georg Cantor Accounting purchased a new computer system for $3,500. The total
resale value after 5 years is estimated to be $525. Using the straight-line method,
Cantor Accounting determined that the computer system would depreciate $595
per year. Use the table above to determine the book value at the end of the third
year.
Possible answers.
(A) $1,690
(B) $1,715
(C) $1,865
(D) $1,940
The book value at the end of the third year is (A) $1,690.
What is depreciation?The depreciation of an asset is the difference between the cost of the asset and the estimated resale value at the end of its useful life.
The straight-line method of depreciation is used to calculate the annual depreciation of an asset.
In this case, the computer system cost $3,500 and was estimated to have a resale value of $525 after five years.
This means that the computer system will depreciate $595 each year.
To calculate the book value at the end of the third year, subtract the depreciation for the first three years from the cost of the asset:
Cost of Computer System: $3,500
Annual Depreciation: -$595
Book Value at End of 3rd Year= $3,500 - ($595 x 3) = $1,690
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According to the data given in the question, the book value at the end of the third year is (A) $1,690.
What is depreciation?The depreciation of an asset is the difference between the cost of the asset and the estimated resale value at the end of its useful life.
The straight-line method of depreciation is used to calculate the annual depreciation of an asset.
In this case,
the computer system cost= $3,500
estimated resale value after five years= $525
depreciation of the computer system each year= $595
To calculate the book value at the end of the third year, subtract the depreciation for the first three years from the cost of the asset:
Cost of Computer System: $3,500
Annual Depreciation: $595
Book Value at End of 3rd Year
= $3,500 - ($595 x 3)
= $1,690
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WOULD LIKE AS SOON AS POSSIBLE PLEASE polynomial multiplication
need answers for 4,5,6,7,8,9, and 10 !
Polynomial multiplication is the process of multiplying two polynomials together to get a new polynomial that represents the product of the two original polynomials.
What is Polynomial multiplication?It should be noted that to multiply two polynomials, you need to perform a distributive operation. You take each term of the first polynomial and multiply it by each term of the second polynomial. Then, you add all the resulting terms together to get the final polynomial.
For example, let's say you want to multiply the polynomials (x + 2) and (x - 3).
First, you multiply the x term in the first polynomial by the x term in the second polynomial:
(x) * (x) = x²
Next, you multiply the x term in the first polynomial by the -3 term in the second polynomial:
(x) * (-3) = -3x
Then, you multiply the 2 term in the first polynomial by the x term in the second polynomial:
(2) * (x) = 2x
Finally, you multiply the 2 term in the first polynomial by the -3 term in the second polynomial:
(2) * (-3) = -6
Now, you add up all the resulting terms to get the final polynomial:
x² - x - 6
Therefore, the product of (x + 2) and (x - 3) is x² - x - 6.
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the student council at deer creak middle school
To reach the goal he student council needs to sell a minimum number of 107 tickets.
What is Sell?Sell means to gave someone something we take money from him. It is a transaction in which product is exchange with product or money. In ancient time we use barter system for transaction.
For raising $400 the student council have to sold each ticket at $4. So the number of ticket sold = $400 / $4 = 100.
They also spent $25 on decorations, so they need to recover that cost too. So, they need to sell an additional tickets = $25 / $4 = 6.25
Since we can not sell 0.25 of a ticket, So we can round the answer to 7.
So that overall total number of tickets that must be sold as 107.
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Complete question:
The student council at Deer Creek Middle School is organizing a dance to raise money for their end-of-year trip. They want to raise at least $400. Tickets are priced at $4 each and they already spent $25 on decorations. What is the minimum number of tickets they have to sell to reach their goal?
10 POINTS! PLEASE HELP! CORRECT ANSWERS ONLY!
Answer:5f+6g+12
Step-by-step explanation:
10f-5f=5f
8+4=12
5f+6g+12
The area of the triangular section is (4, 6, 12, 24) square units. The area of the entire figure is (12, 48, 60, 120) square units
The area of the triangular section is 12 square units and the area of the entire figure is 60 square units.
We know that the Area of triangle is defined as the product of its height to its base.
Area of triangle = height × base
From the figure, we can see that Height is = 4 units and the base is = 6 units,
So, the area of the triangular section is = 1/2 × base × height,
⇒ (1/2) × 6 × 4
⇒ 12 square units
The entire figure consists of two figure , one is a rectangle and the other part is a triangle,
So, the area of the entire figure is = Area of rectangle + area of triangle
⇒ 4×12 + 12
⇒ 48 + 12
⇒ 60 square units
Therefore, the area of the entire figure is 60 square units.
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The given question is incomplete, the complete question is
The area of the triangular section is ___ square units, and the area of the entire figure is ___ square units. Refer to the figure given below.
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-1,9)
(0.-2)
(4,7)
The coordinates of the fourth vertex of the parallelogram are given as follows:
(-5,0).
How to obtain the coordinates of the fourth vertex?To find the coordinates of the fourth vertex of the parallelogram, we need to use the fact that opposite sides of a parallelogram are parallel and equal in length. We can use the given three vertices and their coordinates to find the vector representing one of the sides of the parallelogram, and then use this vector to find the fourth vertex.
For the fourth vertex, we have that:
It is 5 units left of (0, -2), as 4 - (-1) = 5, hence the x-coordinate is of 5.It is 2 coordinates above of (0,-2), as 9 - 7 = 2, hence the y-coordinate is of 0.Hence the coordinates of the vertex are of:
(-5,0).
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PLS HELP! ITS DUE TOMORROW BY 11:59pm
The ratios of the side lengths of B to A, C to B, and D to C are the same. How much more space do the boxes occupy when stored separately in a closet than when they are stacked inside each other in the closet?
1.) Yes, it will fit because the volume of the baseball is 13.36 cubic inches and the volume of the box is 64 cubic inches which is greater than the volume of the baseball.
2) The ratio of the side length of box B to the side length of box A is 1.472 inches: 6 inches.
What is circumference?The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.
To check whether the baseball is will still fit in the box we will check the maximum value of circumference.
[tex]2\pi r = 9.25[/tex]
Make r the subject formula
r= 1.472 inches
Volume of the baseball = [tex]\frac{4}{3\pi x^3}[/tex]
Expand:
13.35 inches^3 < 64 inches^3
So, it will fit inside the box.
2.) [tex]\sqrt[3]{216} = 6[/tex]
Therefore, V = a^3
The length of each side of the box is 6 inches.
The ratio of the side length of box B to the side length of box
A:
1.472 in : 6 inches
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How many pounds of $2. 4/lb trail mix should a grocer combine with 5 lb of $1. 5/lb trail mix to get $1. 9/lb trail mix?
The grocer should combine 3 pounds of $2.4/lb trail mix with 5 pounds of $1.5/lb trail mix to get $1.9/lb trail mix.
Let x be the number of pounds of $2.4/lb trail mix to be added to 5 pounds of $1.5/lb trail mix.
The total amount of trail mix after combining can be expressed as:
x + 5
The total cost of the combined trail mix can be expressed as:
2.4x + 1.5(5) = 1.9(x + 5)
Solving for x, we get:
2.4x + 7.5 = 1.9x + 9.5
0.5x = 2
x = 4
Therefore, the grocer should combine 4 pounds of $2.4/lb trail mix with 5 pounds of $1.5/lb trail mix to get $1.9/lb trail mix.
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Solve for x in the diagram below.
Step-by-step explanation:
Use the triangle bisector theorem:
"The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle."
so 12 is to 16 as x is to 20
12/ 16 = x/20
20 * 12/16 = x = 15 units
Answer:
x = 15
Step-by-step explanation:
the segment inside the triangle is an angle bisector and divides the side opposite the angle into segments that are proportional to the other two sides , that is
[tex]\frac{12}{16}[/tex] = [tex]\frac{x}{20}[/tex] ( cross- multiply )
16x = 12 × 20 = 240 ( divide both sides by 16 )
x = 15
pls answerrrrr
with simple working
Answer:
it goes by minus 8 each time so just put the number and negative 8 each time on a paper and the 20th term would be your answer
A Math student is designing a logo for a Geometry Club that contains 4 triangles contained in a square. The approximate lengths of the legs of the blue triangle in the figure are 12 and 13 mm. What is the approximate length of the hypotenuse of the blue triangle in millimeters? Round to the nearest millimeter, and enter the number only.
Answer:
18mm
Step-by-step explanation:
A^2+B^2=C^2.
144+169=313
square root of 313=17.69≈18mm
DETAILS , LARPCALCL the equation of the circle in standard forn 9x^(2)+9y^(2)+36x-72y+11=0
(x + 2)2 + (y - 4)2 - 11 = 0
The equation of the circle in standard form is x2 + y2 + 36x - 72y + 11 = 0. To arrive at this answer, you need to complete the square for both the x and y terms in the equation. First, divide the equation by 9 to get the following:
x2 + y2 + 4x - 8y + 1 = 0
To complete the square for the x terms, add and subtract (4/2)2 = 16/4 = 4 to the equation:
x2 + 4 + y2 + 4x - 8y + 1 - 4 = -4
Simplifying gives you:
(x + 2)2 + y2 - 8y + 5 = 0
To complete the square for the y terms, add and subtract (8/2)2 = 64/4 = 16 to the equation:
(x + 2)2 + (y - 4)2 + 5 - 16 = -11
Simplifying gives you:
(x + 2)2 + (y - 4)2 - 11 = 0
This is the equation in standard form.
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The function y=100(1. 05)^x represents the cost per night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opened
The given function of the cost represents exponential growth.
Exponential growth: what is it?A form of growth known as exponential growth occurs when the rate of expansion is proportionate to the present value. This implies that the rate of growth increases as the present quantity increases. An exponential function, such as the one in this question (y = abx, where an is the starting value, b is the growth factor, and x is the number of time periods), may be used to describe exponential growth. In natural and social processes, such as population expansion, economic growth, and the spread of illnesses, exponential growth is frequently seen. Yet, there are always resource constraints and other factors that will ultimately reduce or stop the expansion, therefore exponential growth cannot last eternally.
The given function is y=100(1. 05)^x.
To find cost for certain year we substitute different value of x.
From the function we observe that as the value of x increases the function increases continuously.
Hence, the given function of the cost represents exponential growth.
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The complete question is:
1. Which point has the coordinantes(-0. 5, -2. 5)?(1 point)
A. Point a
B. Point b
C. Point c
D. Point d
this is for the quick check in unit 5 lesson 2 for connexus
Point G has the coordinates (-2.5, 5.5), so a correct option is an option (C).
What is a coordinate plane?
The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). It is possible to determine the separation between two points, divide a line into m:n segments, locate a line's midpoint, determine the area of a triangle in the Cartesian plane, and perform other operations using coordinate geometry.
A coordinate plane is a plane in which a set of two number lines are represented, the horizontal line is called the x-axis and the vertical line is called the y-axis.
The given coordinates are (-2.5, 5.5).
The graphical representation of the points is shown below.
Point G has the coordinates (-2.5, 5.5).
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Solve for X.
6x = 18
x = [?]
Answer: 3
Step-by-step explanation: do the opposite function, in this case you need to multiply 6 by x to get 18. So, now you just have to divide 18 by 6.
18/6 =3
You can make sure this is correct by multiplying your numbers of 6 and 3
6x3 = 18
Answer:3
Step-by-step explanation:
6x=6*x
6*x=18
ab=c
in order to find a we need to divide c with a. a=c/b.
in this case,
x=18/6=3
Please help I’ll give brainliest!
Answer: -2x(x-5)(x+4)
Step-by-step explanation:
Answer:
Step-by-step explanation:
add it up and then multiply and then you divide and you got the answer so may i please have brinliest. sir
so its x27
3/5 kilogram of soil fills 1/3 of a container can 1 kilogram of soil fit
in the container
1 kilogram of soil will fit in the container, since 1 kilogram is less than 27/5 kilograms.
What is the fraction of 1 kg soil in the container?
We can start by using ratios to solve this problem.
From the information given, we know that:
3/5 kilogram of soil fills 1/3 of the containerWe want to know how much soil will fit in the entire container (which is equivalent to 3 times the amount that fills 1/3 of the container)
To find out how much soil fills the entire container, we can set up a ratio:
(3/5 kg of soil) : (1/3 of container) = (x kg of soil) : (1 container)
We can cross-multiply to solve for x:
(3/5 kg of soil) * (1 container) = (1/3 of container) * (x kg of soil)
Multiplying both sides by 3/1 gives:
(3/5) * 3 * (1 container) = (1/3) * x
Simplifying gives:
9/5 = 1/3 * x
Multiplying both sides by 3 gives:
27/5 = x
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The complete question is below:
3/5 kilogram of soil fills 1/3 of a container can, 1 kilogram of soil fit ? in the container
What is the equation of a line that is parallel to the line whose equation is y=x+ 2?
Oy-x=-1
O 2x+y = -2
Oy-2x = 3
O x + y = 5
Answer:
[tex]y-x=1[/tex]
Step-by-step explanation:
All the other choices are incorrect because when put in slope-intercept form (y = mx + b), the slope is not equal to 1. The slope of the lines for the other equations are [tex]-\frac{1}{2} , 2, and -1[/tex]. Only the first choice has a slope of 1 like the given equation.
Construct a triangle with the given side lengths. The lines are 5.1, 5.1, and 7.37 centimeters.
A workman is paid #15, 200 for a 40-hours week. Calculate his hourly rate of pay
The workman's hourly rate of pay for a 40-hours week is 380.
Hourly rate of pay = Total pay ÷ Total hours worked
Hourly rate of pay = 15, 200 ÷ 40 = 380
Therefore, the workman is paid 380 per hour for a 40-hours week. To calculate the hourly rate of pay, the total pay is divided by the total hours worked. In this case, the total pay is 15, 200 and the total hours worked is 40, so when we divide 15, 200 by 40, we get 380. This is the hourly rate of pay for the workman for the 40-hours week.
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Use the function below to find F(4). F(x)=5 times (1/3)^x
Answer: 5/81
Step-by-step explanation:
F(4) = 5 * (1/3) ^ 4
F(4) = 5 * 1/81
F(4) = 5/81
Brainliest would be rewarded+100 points!!!
I need this answered fast because I'm on a time limit!!!
Answer:
Add to eliminate X
Step-by-step explanation:
To eliminate a variable, we need to make its coefficient equal and opposite in the two equations. In this case, we can see that the coefficient of x in both equations is the same (6x), so we can eliminate x by adding the two equations.
When we add the two equations, the x term will cancel out, leaving us with the equation:
9y = 36
We can then solve for y by dividing both sides by 9:
y = 4
Now that we know the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
6x + 5y = 12
6x + 5(4) = 12
6x + 20 = 12
6x = -8
x = -4/3
Therefore, the solution to the system of equations is x = -4/3, y = 4.
What is the approximate area of the shaded sector in the circle shown below?
14 in
C
30⁰
OA. 205 in²
O B. 51 in2
OC. 3.67 in²
OD. 7.33 in2
SUBMIT
Answer:
B. 51 in²
Step-by-step explanation:
The area of a sector which has a central angle of θ degrees is given by
Area of circle x θ/360
where
area of circle = πr² with r being the radius
So area of sector = πr² x θ/360
here r = 14 in and θ=30°
Area of sector
= π x 14² x 30/360
= 51.31268 in²
≈ 51 in²
Option B
Leandro wants to build a one-sample z interval with 98% confidence to estimate the proportion of light
bulbs that arrive broken upon shipment to his store. He takes a random sample of 500 bulbs and finds that
25 arrived broken.
What critical value z* should Leandro use to construct this confidence interval?
The critical value for the confidence interval will be 2.33 with a confidence inetrval of 0.05 ± 0.00308
Here we see that the probability to find a bulb from the sample broken is
p = 25/500
= 0.05
Now, we need to build a 98% confidence interval so we will get the critical value to be
(1 - confidence interval)/2
= (1 - 0.98)/2
= 0.02/2
= 0.01
Looking up the value for 0.01 in the standard normal table we the critical value to be
2.33
Now the confidence interval will be
p ± critical value X √[p(1 - p)/n]
= 0.05 ± 0.01√[(0.5 X 0.95)/500]
= 0.05 ± 0.00308
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2. A grocer is weighing watermelons in his grocery
store. The weight in pounds of each watermelon is
listed below. Use the data to create a stem and
leaf plot.
II, 13, 20, 22, 8, 25, 17, 18, 23, 19, 17, 9, 14
Here is the stem and leaf plot :
0 8, 9
1 1, 3, 4, 7, 7, 8, 9
2 0, 2, 3 5
What is a stem and leaf plot?A stem-and-leaf plot is a table that is similar to a histogram. A stem-and-leaf plot divides a number into a stem and a leaf.
The stem is the first number in the digit. In this question, the stem is the tens value. While the leaf is the last number. In this question, it is the units digit. For example in the number 20, 2 would be the stem and 0 would be the leaf. All the numbers that have the same stem would occupy the same row.
An advantage of a stem and leaf plot is that it is easy to create while a disadvantage is that it can be tedious when the dataset is large.
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Given that y varies inversely with x, use the values specified to write an
inverse variation equation relating y to x.
x = -20, y = 2
Please help‼️
Answer:
y = (1/x)+2.05
Step-by-step explanation:
We are only given one point, so there are an infinite number of possible equations. But forging ahead, we can come up with at least one equation of an inverse relationship containing the point (-20,2).
By inversely, the function will produce lower values of y as x increases, or vice versa. A good first step is to say:
y = 1/x
As the value of x increases, the value of y decreases. Invere accomplished.
Simple, elegant, and inverse. If it were a person, she'd be on the cover of People Magazine.
But we want any equation to include the point (-20,2).
Let's see if we can move y=1/x to include (-20,2)
y=(1/x) + b
2 = (1/(-20)) + b
2 = -(0.05) + b
b = 2.05
The equation y = (1/x)+2.05 is an inverse equation that includes point (-20,2).
See the attached graph. Note that when x = 0, the expression (1/x) becomes (1/0). Division by zero is not allowed (undefined). Use caution if in the neighborhood.
Please Show detailed algebraic work.
As a result, it takes around 0.25 minutes for the oven to reach 300°F, or equation roughly 15 seconds. Rounded to the closest minute, the answer is 0 minutes.
What is equation?A math equation is a mechanism for connecting statements and indicating equivalence with both the equals symbol (=). An equation is an algebraic claim that asserts the equivalency of two formulae in algebra. In the calculation 3x + 5 = 14, for example, the equivalence sign separates the numbers 3x + 5 and 14. To explain the relationship among the two words on each surface of a letter, a formula can really be employed. The software and the logo are usually interchangeable. For instance, 2x - 4 equals 2.
Set T = 300 in the equation and solve for t to discover the number of minutes it takes for the oven's temperature to reach 300°F:
T = 400 - It
300 = 400 - It / subtraction T = 300
It = 400 - 300
It = 100
t = 100 / I
T = 400 minus It I = (400 minus T) / t
When we substitute T = 0 and T = 1, we get:
I = (400 - 0) / 1\sI = 400
Now we can substitute I = 400 into the equation we found before for t:
t = 100 / I\st = 100 / 400\st = 0.25
As a result, it takes around 0.25 minutes for the oven to reach 300°F, or roughly 15 seconds. Rounded to the closest minute, the answer is 0 minutes.
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i have the slopes i just need the lengths in radical form and what shape its best described as
Step-by-step explanation:
Im not at a great place to answer them all, but hope this helps on answering them
So the first is 5/2. When you found that, you essentially found the 2 other sides of the "triangle".
You can use Pythagoras to find the length of PQ.
[tex] {2}^{2} + {5}^{2} = {x}^{2} [/tex]
[tex]4 + 25 = 29[/tex]
[tex] \sqrt{29} = x[/tex]
You can either keep it like that, or use a calculator to find that value. im not sure how the system accepts it. you'll do that for each one