The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0. The question is a bit unclear and has multiple parts, so I will answer each part separately.
Part 1: Find the exact value of each of the remaining trigonometric functions of e.
sin 0 = 3/5
cos 0 = 4/5
tan 0 = 3/4
csc 0 = 5/3
sec 0 = 5/4
cot 0 = 4/3
Part 2: Find the lengths and area A.
The length of the arc is 80 * (15/360) = 3.333 yards.
The area of the sector is (80^2 * (15/360))/2 = 266.667 square yards.
Part 3: Find the distance from A to C across the gorge illustrated in the figure.
The distance from A to C is sqrt(170^2 + 170^2) = 240.42 feet.
Part 4: Name the quadrant in which the angle o lies.
The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0.
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Feb 23, 1:45:12 PM Factor the expression completely. 9-36x Answer: Submit Answer
The expression 9-36x can be factorized as 9(1-4x)
An expression's factors are things that are multiplied by other things. A number, variable, phrase, or any other lengthier expression may be used. For instance, 2, x, and y are the factors of 2xy.
To factor the expression 9-36x completely, we need to find the greatest common factor (GCF) of the two terms and then use the distributive property to factor it out.
The GCF of 9 and 36 is 9, so we can factor out 9 from both terms:
9-36x = 9(1-4x)
Now the expression is factored completely.
So the final answer is:
9-36x = 9(1-4x)
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Louis discovers that one variety of carp can grow 5 pounds during each year of its life. He
decides to purchase a very young carp of this variety that weighs 2 pounds.
Define variables and write an equation that represents the relationship between the amount o
time in years that Louis has the carp and the weight of the carp.
The equation which represents the relationship between the variables is; y = 5x + 2.
Which equation represents the situation?As evident in the task content;
To define the variables;
Let x = amount of time in years and
y = weight of the carp.
Since the carp grows 5 pounds each year and initially weighs 2 pounds.
By the slope-intercept form equation;
y = mx + c;
Where,
m = 5 pounds
c = 2 pounds
Therefore, the required relationship which represents the situation is; y = 5x + 2.
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On june 1, 2013, the number of hours of daylight in anchorage alaska was 18 1/4 hours what is the number of hours without daylight??
Answer:
On June 1, 2013, Anchorage, Alaska experiences 18 and 1/4 hours of daylight.
In a 24-hour day, there are 24 - 18 and 1/4 = 5 and 3/4 hours without daylight.
Therefore, the number of hours without daylight on June 1, 2013 in Anchorage, Alaska was 5 and 3/4 hours.
Answer:
24-18.4=5 and3/4
Step-by-step explanation:
what 59 407 rounded to the nearest hundredth
Answer:
59400
Step-by-step explanation:
59407
4 is the hundredth
0 is the number before 4 so it doesn't round up
so it's 59400
Answer:
59,400
Step-by-step explanation:
If it were 59,450 then it would be 59,500 but it is 59.407 witch would mean we are rounding down to 59,400
What is the value of the expression? −16+12 Responses −28 negative 28 −4 negative 4 4 4 28 28
The value of the expression −16 + 12 is −4.
What is subtraction?Subtraction is a basic arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-) and is performed by subtracting the second number from the first number.
We can subtract fractions, decimals, and negative numbers by following the same principles of subtraction.
Here we have
The numerical expression −16 + 12
As we know
12 is 4 greater than 16 and 16 has a negative sign
Therefore,
The value of the expression −16 + 12 is −4.
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Use the 2021 marginal tax rates in the table to compute the tax owed by the person with the given filling status and taxable income single with a taxable income of $57000
Therefore, the total tax owed by a Single filer with a taxable income of equation $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.
What is equation?When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.
Assuming that the taxable income of $57,000 is for the tax year 2021 and the person is filing as Single, we can use the following marginal tax rates to compute the tax owed:
Tax Rate Taxable Income Range
10% $0 - $9,950
12% $9,951 - $40,525
22% $40,526 - $86,375
24% $86,376 - $164,925
32% $164,926 - $209,425
35% $209,426 - $523,600
37% $523,601 or more
To compute the tax owed, we need to apply each tax rate to the corresponding portion of the taxable income and add up the results. Here's how we can do that:
The first $9,950 of taxable income is taxed at 10%, so the tax on this portion is $9950 x 0.1 = $995.
The next $30,575 ($40,525 - $9,950) of taxable income is taxed at 12%, so the tax on this portion is $30,575 x 0.12 = $3,669.
The remaining $17,475 ($57,000 - $40,525) of taxable income is taxed at 22%, so the tax on this portion is $17,475 x 0.22 = $3,844.50.
Therefore, the total tax owed by a Single filer with a taxable income of $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.
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Suppose a researcher wishes to study how exercise and diet affect weight loss. The researcher collects data from 12 volunteers with similar weights and health conditions. All the partic- ipants are randomly assigned to one of the following three programs: Program I with diet only, Program II with exercise only, and Program III with combinations of diet and exer- cise. After three months, the weight loss (in pounds) of each participant is recorded and summarized as follows: Program 1: 2,0, 1, 1
Program II: 1, 2,1 Program III: 3, 2, 1, 4, 4 a) The researcher thinks that the three programs should not be equally effective. Please carry out a nonparametric test at a significant level of 0.05 to examine the effectiveness of the three programs. You can either do the calculation by hand or use R to get the results. b) The researcher also hopes to show that Progam III is more effective than Program I in weight loss. Please carry out a nonparametric test at a significant level of 0.05 to examine the effectiveness of the two programs. You can either do the calculation by hand or use R to get the results.
The researcher's study aims to examine how exercise and diet affect weight loss. The researcher collected data from 12 volunteers with similar weights and health conditions and randomly assigned them to one of three programs: Program I with diet only, Program II with exercise only, and Program III with a combination of diet and exercise. After three months, the weight loss of each participant was recorded and summarized. The researcher wishes to carry out nonparametric tests at a significant level of 0.05 to examine the effectiveness of the three programs and to compare the effectiveness of Program III to Program I.
a) To examine the effectiveness of the three programs, we can use the Kruskal-Wallis test, a nonparametric test that compares the medians of three or more groups. The null hypothesis is that the medians of the three programs are equal, and the alternative hypothesis is that at least one of the medians is different. We can use the R function kruskal.test() to carry out the test:
```
> weight_loss <- c(2,0,1,1,1,2,1,3,2,1,4,4)
> program <- factor(c(rep("I",4), rep("II",3), rep("III",5)))
> kruskal.test(weight_loss ~ program)
```
The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of the three programs.
b) To compare the effectiveness of Program III to Program I, we can use the Wilcoxon rank-sum test, a nonparametric test that compares the medians of two groups. The null hypothesis is that the medians of Program III and Program I are equal, and the alternative hypothesis is that the medians are different. We can use the R function wilcox.test() to carry out the test:
```
> weight_loss_I <- c(2,0,1,1)
> weight_loss_III <- c(3,2,1,4,4)
> wilcox.test(weight_loss_I, weight_loss_III)
```
The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of Program III and Program I.
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RADICALS Solving an equation usir Solve x^(3)=-13 where x is a rea Simplify your answer as much a
To solve the equation x^(3) = -13, we need to take the cube root of both sides of the equation. The cube root of x^(3) is x, and the cube root of -13 is -2.3513 (rounded to 4 decimal places). Therefore, the solution to the equation is x = -2.3513.
Here are the steps to solve the equation:
1. Start with the equation x^(3) = -13
2. Take the cube root of both sides of the equation: (x^(3))^(1/3) = (-13)^(1/3)
3. Simplify the left side of the equation: x = (-13)^(1/3)
4. Calculate the cube root of -13: x = -2.3513 (rounded to 4 decimal places)
So the solution to the equation is x = -2.3513.
Note: The original question had some typos and irrelevant parts, so I ignored those and focused on the main equation to solve.
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True or false let be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that equals 8 is denoted by
The given statement " let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 will be denoted by P(X=8)" is true. Because In probability theory, P(X=8) denotes the probability that the random variable X takes on the value 8.
Probability is a measure of the likelihood or chance that a certain event or outcome will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
In this case, X represents the number of male births between 1:00am and 3:00am at a hospital in Orange County. So, P(X=8) represents the probability that exactly 8 male births occur during that time period.
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--The given question is incomplete, the complete question is
"True or false let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 is denoted by P(X=8)"--
Summary
How can the correlation coefficient help you determine how right (or justified) you are in using a line to
represent data?
The correlation coefficient, denoted by r, tells us how closely data in a scatterplot fall along a straight line. The closer that the absolute value of r is to one, the better that the data are described by a linear equation. If r =1 or r = -1 then the data set is perfectly aligned. Data sets with values of r close to zero show little to no straight-line relationship.
Due to the lengthy calculations, it is best to calculate r with the use of a calculator or statistical software. However, it is always a worthwhile endeavor to know what your calculator is doing when it is calculating. What follows is a process for calculating the correlation coefficient mainly by hand, with a calculator used for the routine arithmetic steps.
do it to be the smartest (image attach)
Answer: a = 20°
Step-by-step explanation:
We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. We will write an equation to solve.
a = 180° - 90° - 70°
a = 20°
Answer:
20 degrees
Step-by-step explanation:
Straight Angle: 180 degrees
You know that there is a right angle which is 90 degrees. You can subtract 180 by 90 to get 90. Then you are given an angle measurement of 70 degrees. Subtract 70 from 90 to get 20.
20 is the measure of the missing angle
Can anyone help me in my math homework 55 points I’ll send you 50 more if u can help
The ordered pairs are the solution to the inequality as follows:
6) (-1,3) and 7) (1,4).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per the question, we have:
5) (0,-1)
No, this ordered pair is not a solution to the inequality.
6) (-1,3)
Yes, this ordered pair is a solution to the inequality.
7) (1,4)
Yes, this ordered pair is a solution to the inequality.
8) (0,0)
No, this ordered pair is not a solution to the inequality.
9) (3,3)
No, this ordered pair is not a solution to the inequality.
10) (2, 1)
No, this ordered pair is not a solution to the inequality.
Thus, the ordered pairs are the solution to the inequality as follows:
6) (-1,3) and 7) (1,4).
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Use substitution to solve
Answer:
x=4, y=5
Step-by-step explanation:
[tex]x=2y-6\\ x-2y=-6\\\\y=3x-7\\y-3x=-7\\\\\\\\-3x+y=-7\\-3(2y-6)+y=-7\\-6y+18+y=-7\\-5y+18=-7\\-5y=-25\\y=5\\\\\\x=2y-6\\x=2(5)-6\\x=4[/tex]
the dimensions of a rectangle are 19 1/2 cm by 21 1/4 cm what is the area of the triangle
Answer: 207.1875
Step-by-step explanation:
side length a = 19.5 cm
side length b = 21.25 cm
diagonal p = q = 28.841159824112 cm
perimeter P = 81.5 cm
area of rectangle A = 414.375 cm2
area of rectangle divided into a triangle = 207.1875
hope this helps
If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone
The diameter of the opening of the cone is approximately 8.92 units.
We can use the formula for the volume of a cone:
V = (1/3) × π × r^2 × H
where V is the volume, H is the height, and r is the radius of the base.
In this case, we are given the volume V = 196 and the height H = 12. We want to find the diameter of the opening, which is 2r.
First, we can rearrange the formula for the volume to solve for r
r = sqrt((3V) / (πH))
Plugging in the values, we get
r = sqrt((3 × 196) / (π × 12)) ≈ 4.46
So the radius of the base of the cone is approximately 4.46 units.
Finally, we can find the diameter of the opening:
d = 2r ≈ 8.92 units
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The given question is incomplete, the complete question is:
The volume of the cone is 196 cubic units. If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone?
what is the ratio 28:20 simplified
One solution to a quadratic function, g, is given.
9 - √2i
Which statement is true?
A. Function g has no other solutions.
B. The other solution to function g is -9 + √2i
.
C. The other solution to function g is -9 - √2i
.
D. The other solution to function g is 9 + √2i
.
Answer:
D. The other solution to function g is 9 + √2i
Step-by-step explanation:
The roots of a quadratic equation of the form ax² + bx + c = 0
are
[tex]x = -\dfrac{b}{2a} + \dfrac{\sqrt{b^2-4ac}}{2a}\\and\\x = -\dfrac{b}{2a} - \dfrac{\sqrt{b^2-4ac}}{2a}\\[/tex]
If one of the roots is 9 - √2i then
[tex]-\dfrac{b}{2a} = 9[/tex]
and
[tex]\dfrac{\sqrt{b^2-4ac}}{2a} = 2i[/tex]
So if one root is 9 - √2i then the other root must be 9 -+ 2i
This is answer choice D
roots in simplest form by completing the square: -5x^(2)-80x-140=0 Submit Answer
The roots in simplest form are x=-8+6i and x=-8-6i.
The question is asking you to find the roots of -5x^(2)-80x-140=0 in simplest form by completing the square.
To complete the square, follow the steps below:
1. Divide the coefficient of the x^2 term by 2 and add the result to both sides of the equation:
-5x^2/2 + 80x/2 + 140 = 0 + 5x^2/2
2. Square the coefficient of the x^2 term: (5x^2/2)^2
3. Add this result to both sides of the equation: 5x^2/2 + (5x^2/2)^2 + 80x/2 + 140 = 5x^2/2 + (5x^2/2)^2
4. Rewrite the equation as a perfect square on the left side of the equation: (5x^2/2 + 40x/2)^2 = (5x^2/2 + 40x/2)^2 + 140
5. Take the square root of both sides to solve for x:
5x^2/2 + 40x/2 = ± √140
6. Rewrite the equation as two equations in x:
x = -80 ± √140 / 10
7. Simplify:
x = -8 ± √14 / 1
Therefore, the roots of -5x^(2)-80x-140=0 in simplest form by completing the square are x = -8 ± √14 / 1.
To find the roots in simplest form by completing the square for the equation -5x^(2)-80x-140=0, we need to follow these steps:
1. First, we need to isolate the x terms on one side of the equation. We can do this by adding 140 to both sides of the equation:
-5x^(2)-80x=140
2. Next, we need to factor out the coefficient of the x^(2) term, which is -5:
-5(x^(2)+16x)=-140
3. Now we need to complete the square by adding the square of half of the coefficient of the x term to both sides of the equation:
-5(x^(2)+16x+64)=-140+320
4. Simplify the right side of the equation:
-5(x+8)^(2)=180
5. Divide both sides of the equation by -5:
(x+8)^(2)=-36
6. Take the square root of both sides of the equation:
x+8=±6i
7. Solve for x:
x=-8±6i
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write an expression by expanding -5(-2d + 6)
Answer:
See below.
Step-by-step explanation:
We are asked to "expand", rather distribute the expression.
We can Distribute due to the Distributive Property.
What is the Distributive Property?
The Distributive Property is a property that allows us to distribute the multiplier into numbers in the parentheses.
Let's distribute for this expression.
Distribute:
[tex]-5(-2d + 6)=(-5 \times -2d)+(-5 \times 6)= 10d -30[/tex]
Our distributed expression is 10d - 30.
HELPP! NEED NOW!!! ASAP!!
The volume of a rectangular prism is 208 cm³. If the area of one end is 16 cm², what is the length of the prism? (FOUND ANSWER)
The length of the rectangular prism is 13 centimetres.
How to find the side of a rectangular prism?The volume of a rectangular prism is 208 cm³. The area of one end is 16 cm². The length of the rectangular prism can be found as follows:
Therefore,
volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightHence, let's find the length
volume of a rectangular prism = lwh
208 = 16 × l
16l = 208
divide both sides by 16
l = 208 / 16
l = 13 cm
Therefore,
length of the prism = 13 cm
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Two weather stations are aware of a thunderstorm located at point c. The weather stations A and B are 34 miles apart. How far is weather station A from the storm?
The distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles, which can be calculated using the Pythagorean theorem.
What is the Pythagorean theorem?The Pythagorean Theorem is an equation in geometry which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse.
Weather station A is 34 miles away from the thunderstorm located at point c. To measure the distance between weather station A and the storm, we must calculate the hypotenuse of a right triangle. The right triangle is formed by the two points of the storm and weather station A, with the 34 miles between them forming the base of the triangle. The hypotenuse of the triangle is the distance between the two points, which can be calculated using the Pythagorean theorem. The equation for the Pythagorean theorem is a² + b²= c², where a and b are the sides of the triangle, and c is the hypotenuse.
Therefore, the distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles.
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Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e}. If A = {1,
2, a, e} and B = {1, 2, 3, 4, a, b, c}, find the following.
(c) n(A ∪ Bc)
(d) n(Ac ∩ Bc)
The answers are n(A ∪ Bc) = 10 and n(Ac ∩ Bc) = 6.
To solve this question we need knowledge of set theory, union and intersection.
(c) To find n(A ∪ Bc), we first need to find the complement of B, which is Bc = {5, 6, 7, 8, 9, d, e}. Now, we can find the union of A and Bc, which is A ∪ Bc = {1, 2, a, e, 5, 6, 7, 8, 9, d}. The number of elements in this set is n(A ∪ Bc) = 10.
(d) To find n(Ac ∩ Bc), we first need to find the complement of A, which is Ac = {3, 4, 5, 6, 7, 8, 9, b, c, d}. Now, we can find the intersection of Ac and Bc, which is Ac ∩ Bc = {5, 6, 7, 8, 9, d}. The number of elements in this set is n(Ac ∩ Bc) = 6.
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In order to gaph the ine whote equition iay=52x+2, begin by ploeing the port Fromi ins pointi ne miove wits up the rese) and insts to the righe che runl. Fa in each blopk so thut the reseinng statement is true. In order to arach the ine whose equason isy=52x+3, begn by plotting the point: From this point, we mere units up (ehe fise) and unis to the right (the run). In ceder to graph the ine whose eqaston isy=52x+3, begin by ploting the poun From this point, we move Units up (the risel and unis to the tight (the nun).
This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.
In order to graph the line whose equation is y=5/2x+2, we need to begin by plotting the point (0,2) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.
Similarly, to graph the line whose equation is y=5/2x+3, we need to begin by plotting the point (0,3) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.
In both cases, the slope of the line is 5/2, which is the coefficient of x in the equation. The slope tells us how much the line rises or falls for every unit it moves to the right. In this case, the line rises 5 units for every 2 units it moves to the right. This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.
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Charlotte wants to know which website has more user engagement per a
single writer.
1) Charlotte thought of two different ways to define this quantity. Identify
these two definitions among the following options.
A. Avg number of likes per writer
B. Total number of comments
C.Avg number of people words per writer
D. Avg number of comments per writer
The average number of likes per writer and the average number of comments per writer can be used to determine which website has more user engagement per a single writer
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the average number of likes per writer be L
Let the average number of comments per writer be C
Now , the number of writers for website A = 5
The number of writers for website B = 11
The average number of likes per post for A = 3500 likes
So , the average number of likes per writer A = ( 3500 / 5 ) = 700 likes
And , the average number of likes per writer B = ( 3500 / 5 ) = 700 likes
The number of comments per writer A = ( 500 / 5 ) = 100 comments
The number of comments per writer B = ( 450 / 11 ) = 40.90 comments
Hence , the average number of likes per writer and the average number of comments per writer are solved
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A rectangular cedar chest measures 40 inches long by 22 inches wide by 20 inches high.
Part A
Find the volume of the chest.
Part B
A cushion is made to cover the top of the chest. Calculate the area of the chest that the cushion covers.
Part C
Explain any difference in the units for the volume and the area.
(A). The chest has a volume of 17,600 cubic inches. (B). The cushion covers 880 square inches of the chest. (C). Whereas area is measured in square units, volume is measured in cubic units.
What is the straightforward meaning of area?An object's area is determined by its shape. The amount of space a figurine or any other as double geometric shape takes up on a plane depends on its area.
(A). Chest volume is calculated as follows: 40 inches by 22 inches by 20 inches, or 17,600 cubic inches.
(B). The cushion's coverage area for the chest is 40 inches by 22 inches, or 880 square inches.
(C). The units for area are square units, while the units for volume are cubic elements (like as cubic feet or cubic meters) (such as square inches or square meters). This is so because area is the measure of space an item occupies in two dimensions, but capacity means the quantity of space an object occupies in three dimensions. As a result, area is expressed in feet or meters whereas volume is recorded in cubic units.
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$13.50 discounted 75%
Answer: 75% of $13.50 is 10.125
Step-by-step explanation:
Answer:
10.125
Step-by-step explanation:
13.50 x .75 = 10.25
PLEASE HELP
A group of people living in either an apartment or a house are asked whether they own a pet or not. The data are collected in the table.
Pet No pet
Apartment 18 36
House 43 24
Drag and drop the correct percentages into each box to complete each statement.
Of the people living in an apartment, about _______ have a pet. Of the people living in a house, about______have no pet.
30%
33%
36%
40%
60%
64%
67%
70%
Answer:
Step-by-step explanation:
Firstline = 33%
Second line = 36%
Answer:
Firstline = 33%
Second line = 36%
Step-by-step explanation:
Why might a person open a savings account?
Will mark brainliest
A) Savings accounts are designed for a short term such as paying monthly bills.
B)Savings accounts provide high interest rates in exchange for taking on a great deal of risk.
C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.
D)Savings accounts provide a quick way to pay monthly bills.
Answer:
C) Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank. Savings accounts provide a safe and secure way to store money for use in the future. They also offer the opportunity to earn interest over time, which can be used to grow your savings. As a result, savings accounts are a great way to save for long-term goals such as retirement, a child's education, or a down payment on a home.
Answer:
C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.
Step-by-step explanation:
Savings accounts are designed to keep your money safe and to hold it for as long as you want. Ex for the future, such as collage or something you really want like a car. A saving account will will hold your money until you want to deposit it out of your account.
What is the fourth term in the geometric sequence 3, –9, 27, … ?
The fourth term in the geometric sequence is -81.
What is a geometric sequence?
In mathematics, a geometric progression, also known as a geometric sequence, is a set of non-zero numbers where each term after the first is derived by multiplying the previous one by a fixed, non-zero amount called the common ratio.
We are given a sequence as 3, –9, 27, ...
We can observe that each term is being multiplied by -3.
So, the common ratio i.e. r = -3
Here x = 4 and a₁ = 3.
Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get
⇒a₄ = a₁ r⁽⁴⁻¹⁾
⇒a₄ = a₁ r³
⇒a₄ = 3 (-3)³
⇒a₄ = 3 * -27
⇒a₄ = -81
Hence, the fourth term in the geometric sequence is -81.
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HELP ASAPPPPPP PLESS
The coordinates of the vertices of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) .
The coordinates of the vertices of △R′S′T′ are R′(3, −3) , S′(3, −1) , and T′(−1, −4) .
What is the sequence of transformations that maps △RST to △R′S′T′?
A sequence of transformations that maps △RST to △R′S′T′ is a (answer choice) area followed by a (answer choice) area
options:
translation 4 units right
rotation of about 180 degrees of origin
rotation 90 degrees clockwise about the origin
reflection across the y=x line
Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.
Which branches of mathematics employ coordinates?an arrangement of elements that faithfully represent an angle. The first number on a graph indicates the distance along, while the second number indicates the distance up or down. The point (12,5), for instance, is situated 12 below and 5 above.
A sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.
Explanation:
First, we need to reflect the original triangle RST across the y=x line. This will result in a new triangle that is congruent to the original one but with its vertices in different positions. The new vertices will be R(-1, -3), S(-1, -1), and T(-5, -4).
Next, we need to rotate this new triangle 90 degrees clockwise about the origin. This will result in another new triangle that is congruent to the previous one but with its vertices in different positions. The new vertices will be R'(3, -3), S'(3, -1), and T'(-1, -4), which are the vertices of △R′S′T′.
Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.
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