Answer:
13.2 cm
Step-by-step explanation:
Use Pythagorean Theorem
Hypotenuse^2 = (leg1)^2 + (leg2)^2
H^2 = 13^2 + 2^2
= 169 + 4
H^2 = 173
H = sqrt (173) = 13.2 cm
In gym class, a student can do 30 sit-ups in 60 seconds and 90 sit-ups in 180 seconds.
Graph the proportional relationship.
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 120 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.
What is a graph?A graph can be defined as a type of chart that's commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.
Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.Furthermore, the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.
In this context, we can reasonably infer and logically deduce that the relationship between the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of this graph is proportional and given by this equation:
y = 3x
Where:
y represent the number of sit-ups.x represent the time.Read more on graphs here: brainly.com/question/4546414
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Answer:
A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.
Step-by-step explanation:
Your family decides to go out to dinner to celebrate your brothers graduationfrom high school. The family's meal cost $75. Your waitress did a great job andyour parents decide to leave her a 20% tip. How much tip money should yourparents leave her if they leave her 20%? And what is the total cost of the meal? *
$75 -----> 100%
x ---------> 20%
[tex]\begin{gathered} x\times100=75\times20 \\ 100x=1500 \\ \frac{100x}{100}=\frac{1500}{100} \\ x=15 \end{gathered}[/tex]asnwer 1: they leave her $ 15
answer 2: the total cost of the meal is
[tex]75+15=90[/tex]$ 90
how do i use a graphing calculator to solve the system.
Given:
[tex]\begin{gathered} 0.4x\text{ + }\sqrt{2}y\text{ = 1} \\ \sqrt{5}\text{ x + 0.8y = 1} \end{gathered}[/tex]Using a graphing calculator, we have the graph shown below:
The point of intersection of the equations represents the solution to the system.
Hence, the solution to the system is:
x = 0.216
y = 0.646
You roll a six-sided die twice. What is the probability of rolling an even number and then an odd number?A)1B)1/3 큼C)nilaD)
Let's begin by listing out the given information:
A fair dice has 6 sides
The dice has its sides numbered from 1-6
The number of sides with even numbers (2, 4 & 6) equals 3
The number of sides with odd numbers (1, 3 & 5) equals 3
The probability of rolling an even number is given as shown below:
[tex]\begin{gathered} P=\frac{Number\text{ of Possible Outcome}}{Total\text{ Number of Outcome}} \\ P\mleft(even\mright)=\frac{3}{6}=\frac{1}{2} \\ P(even)=\frac{1}{2} \end{gathered}[/tex]The probability of rolling an odd number is given as shown below:
[tex]\begin{gathered} P=\frac{Number\text{ of Possible Outcome}}{Total\text{ Number of Outcome}} \\ P(odd)=\frac{3}{6}=\frac{1}{2} \\ P(odd)=\frac{1}{2} \end{gathered}[/tex]The probability of rolling an even number followed by an odd number is obtained by the product of the probabilities above. We have:
[tex]\begin{gathered} P(even,odd)=P(even)\times P(odd) \\ P(even,odd)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ P(even,odd)=\frac{1}{4} \end{gathered}[/tex]Therefore, the probability of rolling an even number and then an odd number is 1/4
the perimeter of a rectangle is a rational number. the length of a rectangle is 6 units. the width of a rectangle must be a/an rational/irrational (circle one) number.
A rational number
Explanations:The perimeter of a rectangle is given by the formula:
Perimeter = 2(Length + Width)
The Length = 6 units
Perimeter = 2 (6 + Width)
Perimeter = 12 - 2 Width
2 Width = 12 - Perimeter
Width = (12 - Perimeter)/2
Note that a rational number is a number that can be written as a fraction of two integers.
Since the perimeter is said to be a rational number, any rational number substituted into the formula equation for the width above will give a rational number.
The width of the rectangle is therefore a rational number
6 minus 3 times a number is less than 30. Find the number:
x > -8
Explanations:Let the number be represented by x:
Three times the number = 3x
Six minus three times the number = 6 - 3x
Six minus three times the number is less than 30:
That can be interpreted mathematically as:
6 - 3x < 30
To find the value of x:
Step 1: Collect like terms
- 3x < 30 - 6
-3x < 24
Step 2: Divide both sides by 3:
[tex]\frac{-3x}{3}=\text{ }\frac{24}{3}[/tex]-x < 8
Multiply both sides by (-1) and change the < sign to >
(-1) (-x) > 8 x(-1)
x > -8
What is the factor 24/28 in simplest form
Answer:
6/7
Step-by-step explanation:
24/28 they both are commonly divisible by 4,
making them 6/7
food cost for your restaurant is about $.38 on the dollar. that means for every dollar in sales, you spend 38 cents in food cost.figure out the food cost for the following days’ sales:monday:$3,459.00tuesday:$2,976.81wednesday:$3,185.32thursday:$3,562.91friday:$4,582.13saturday:$4,820.36
The Solution.
Monday's sales is $3459.00
The food cost for Monday is
[tex]\text{ Food cost = 0.38}\times3459=\text{ \$1314.42}[/tex]Tuesday's sales is $2976.81
The food cost for Tuesday is
[tex]\text{Food cost = 0.38}\times2976.81=\text{ \$}1131.19[/tex]Wednesday's sales is $3185.32
The food cost for Wednesday is
[tex]\text{ Food cost = 0.38}\times3185.32=\text{ \$}1210.42[/tex]Thursday's sales is $3562.91
The food cost for Thursday is
[tex]\text{Food cost = 0.38}\times3562.91=\text{ \$}1353.91[/tex]Friday's sales is $4582.13
The food cost for Friday is
[tex]\text{Food cost = 0.38}\times4582.13=\text{ \$}1741.21[/tex]Saturday's sales is $4820.36
The food cost for Saturday is
[tex]\text{Food cost = 0.38}\times4820.36=\text{ \$}1831.74[/tex]Deck PlanOutside* EdgeWall A10 feetDoorway13 feet-10 feetWall BThe deck will have the shape of one fourthof a circle. What is the best estimate of thearea (A) of this deck?(Area of circle = tr2)πr)(Use 3.14 for it.)
18) the best estimate will be 75 square feet (option G)
Explanation:18) radius = 10ft
let π = 3.14
We are told the deck will have 1/4 the area of a circle. We need to first find the area of a circle.
Area of circle = πr²
[tex]\begin{gathered} Area\text{ of circle = 3.14 }\times\text{ 10}^2 \\ Area\text{ of circle = 314 ft}^2 \end{gathered}[/tex]Next, we will divide the area by 4:
[tex]\begin{gathered} Area\text{ of the deck = }\frac{area\text{ of circle}}{4} \\ Area\text{ of the deck = }\frac{314}{4} \\ \\ Area\text{ of the deck = 78.5 ft}^2 \end{gathered}[/tex]From the options, the one close to the result we got is 75 square feet
Hence, the best estimate will be 75 square feet (option G)
Factor the following polynomials completely.(x + y)³ + 1 =
Given the equation (x + y)³ + 1 , we can assume we have two terms here. These are (x + y)³ and 1. Since both terms are perfect cubes, we can use the sum of cubes formula which is:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]where a = (x+y) and b = 1.
Therefore, the factors of (x + y)³ + 1 is:
[tex]\begin{gathered} \mleft(x+y\mright)^3+1=(x+y+1)\lbrack(x+y)^2-(x+y)(1)+1^2) \\ (x+y)^3+1=(x+y+1)(x^2+2xy+y^2-x-y+1) \end{gathered}[/tex]The factor of (x + y)³ + 1 is (x + y + 1)(x² + 2xy + y² - x - y +1).
1 pointThe 5 consecutive integers below add up to 175. What is the value of x?x-3x-2X - 1ХX + 1
Then x=36.
A pizza is to be cut into halves. Each of these halves is to be cut into fourths. What fraction of the pizza is each of thefinal pieces?
Given:
Each of these halves is to be cut into fourths.
So:.
A pizza is to be cut into halves
since half is represented by 1/2.
So each piece is now
[tex]\frac{1}{2}\text{ of the original.}[/tex]If each of these halves is to be cut into fourths, then the fraction of final pieces is:
[tex]\begin{gathered} =\frac{1}{2}\times\frac{1}{4} \\ =\frac{1}{8} \end{gathered}[/tex]
Answer:
1/8
Step-by-step explanation:
Fractions
We have 1/2
!/2 is to be cut in 1/4
1/2 * 1/4 = 1/8
Nicholas and Jack volunteer to fill gift boxes for soldiers serving overseas. Both work at a constant rate. They work together for 6 hours and fill 126 boxes. Nicholas fills 9 boxes every hour. How many boxes does Jack fill every hour?
Firstly, we need to know the number of boxes they both filled per hour.
From the question, we are told that 126 boxes were filled in six hours; thus in an hour, the number of boxes filled will be 126/26 = 21 boxes
Now in an hour, Nicholas filled 9 boxes; the number of boxes that will be filled is clearly the remainder of the 21 boxes.
The number of boxes filled by Jack is thus; 21 - 9 = 12 boxes
Jack fills 12 boxes in an hour
if 3x +6 = 18 what is 10x -2
38
1) Starting from the first equation
3x +6 = 18 Subtract 6 from both sides
3x = 18 -6
3x = 12 Divide both sides by 3
x =4
2) Since x =4, let's plug that into the second expression 10x -2 to find out "what is 10x -2"
10x -2 Replace x, by 4
10(4) -2 Effectuate the multiplication
40 -2
38
Hence, the answer is 38
The area of the triangle is 330 square feet.The height of the triangle is ___
Answer:
22 feet
Explanation:
The area of a triangle can be calculated using the following equation:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the base and h is the height.
We know that the area is 330 square feet and the base is 30 ft, so we can replace these values to get:
[tex]330=\frac{30\times h}{2}[/tex]Now, we can solve the equation for h. First, multiply both sides by 2:
[tex]\begin{gathered} 2\times330=2\times\frac{30\times h}{2} \\ 660=30\times h \end{gathered}[/tex]Then, divide both sides by 30:
[tex]\begin{gathered} \frac{660}{30}=\frac{30\times h}{30} \\ 22=h \end{gathered}[/tex]Therefore, the height of the triangle is 22 feet.
Exponential Regression
The table below shows the population, P. (in thousands) of a town after 12 years.
0
72
P 2400
3
2801.27
7
3608.71
12
14
4974.15 5426.17
19
6898.37
(a) Use your calculator to determine the exponential regression equation P that models the set of
data above. Round the value of a to two decimal places and round the value of b to three decimal
places. Use the indicated variables.
P =
(b) Based on the regression model, what is the percent increase per year?
96
(c) Use your regression model to find P when n = 13. Round your answer to two decimal places.
The population of the town after
P =
thousand people
(d) Interpret your answer by completing the following sentence.
years is
thousand people.
Considering the given table, it is found that:
a. The exponential regression equation is: P(t) = 2408.80(1.059)^t.
b. The yearly percent increase is of 5.9%.
c. P(13) = 5075.
d. The population of the town after 13 years is of 5075.
How to find the exponential regression equation?The exponential regression equation is found inserting the points into a calculator.
The points are given as follows:
(0, 2400), (3, 2801.27), (7, 3608.71), (12, 4974.15), (14, 5426.17), (19, 6898.37).
Using a calculator, the function is:
2408.80(1.059)^t.
The yearly percent increase rate is calculated as follows:
1 + r = 1.059
r = 1.059 - 1
r = 0.059
r = 5.9%.
Then in 13 years, the population will be given as follows:
P(13) = 2408.80(1.059)^13 = 5075.
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Determine which point is the solution to the given system. y= -7/2 x + 32 y= 4/5 x -11
Answer:
(10, -3)
Step-by-step explanation:
[tex]-\frac{7}{2}x+32=\frac{4}{5}x-11 \\ \\ -35x+320=8x-110 \\ \\ -43x=-430 \\ \\ x=10 \\ \\ \therefore y=-\frac{7}{2}(10)+32=-3[/tex]
Araceli filled a cone-shaped container with a variety of colored sand to give as a gift to a friend. The volume of a cone is represented by the expression below, where r is the radius of the base of the cone and h is the height of the cone.radius = 3 1/23 5/3 is the height
The volume of the cone is 45.28 cubic inches.
The amount of sand inside the cone is measured by its volume.
Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.
The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.
The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]
The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]
The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]
So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]
[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]
The volume of the cone is 45.28 cubic. inches
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Suppose that y varies inversely with x, and y = 5/4 when x = 16.(a) Write an inverse variation equation that relates x and y.Equation: (b) Find y when x = 4.y =
In general, an inverse variation relation has the form shown below
[tex]\begin{gathered} y=\frac{k}{x} \\ k\to\text{ constant} \end{gathered}[/tex]It is given that x=16, then y=5/4; thus,
[tex]\begin{gathered} \frac{5}{4}=\frac{k}{16} \\ \Rightarrow k=\frac{5}{4}\cdot16 \\ \Rightarrow k=20 \end{gathered}[/tex]Therefore, the equation is y=20/x
[tex]\Rightarrow y=\frac{20}{x}[/tex]2) Set x=4 in the equation above; then
[tex]\begin{gathered} x=4 \\ \Rightarrow y=\frac{20}{4}=5 \\ \Rightarrow y=5 \end{gathered}[/tex]When x=4, y=5.
I need to explain the mistake he made and show my work and I need the answer
The problem is;
-2(x-1) - 2 > 8 - 5x +4+ x
open the parenthesis
-2x + 2 -2 > 8- 5x + 4+ x
collect the like-term
-2x+5x-x > 8+4
2x > 12
divide both-side of the inequality by 2
x>6
The first mistake that was made is adding of the x-variables
It is 2x and not -6x
2/3 divided 17/28 equals what?
A batting cage charges a flat fee of $5 to practice and th Write an equation that models the charges (C) in terms of the number of bucket balls (b) that you use: O C = 1.50 b + 5 O C = 5 b + 1.50 6 Ob = 1.60 C + 5 Ob = 5 C + 1.50
we have
C -----> total charge
b -----> number of buckets of balls
Remmeber that
the equation of the line in slope intercept form is equal to
y=mx+b
where
m is the slope and b is the initial value or y-intercept
In this problem
m=$1.50 per buckey
b=$5
therefore
y=1.50x+5
or
C=1.50b+5
answer is first option
Solve the inequality and write the solution using:
Inequality Notation:
The answer of the given inequality is x < 16
Difference between equality and inequality equations
Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The inequality expression is ,
(1 * x) /4 < 4 or x/4 < 4
=> x < 4 * 4
=> x < 16
Therefore, the answer is x < 16.
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Determine weather it is a function, and state it’s domain and range.
Find the inverse of:
[tex]f(x)=(3x-24)^2[/tex]The variable x can take any real value and the function f(x) exists. This means
the domain of f(x) is (-∞, +∞).
Now find the inverse function.
[tex]\begin{gathered} y=(3x-24)^2 \\ \pm\sqrt[]{y}=3x-24 \\ \pm\sqrt[]{y}+24=3x \\ x=\frac{\pm\sqrt[]{y}+24}{3} \\ x=\pm\frac{1}{3}\sqrt[]{y}+8 \end{gathered}[/tex]Swapping letters, we get the inverse function:
[tex]y=\pm\frac{1}{3}\sqrt[]{x}+8[/tex]For each value of x, we get two values of y, thus this is not a function.
The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)
The range of the inverse is the domain of the original function, that is, (-∞, +∞)
Function: No
Domain: [0, +∞)
Range: (-∞, +∞)
The choice to select is shown below.
pls help????? –2x = –20y + 18
Answer:
y = 1/10x + 9/10
Step-by-step explanation:
Find slope intercept form: –2x = –20y + 18
slope intercept form: y = mx + b
_______________________________
–2x = –20y + 18
add 20y to both sides:
–2x + 20y = –20y + 18 + 20y
–2x + 20y = 18
add 2x to both sides:
–2x + 20y + 2x = 18 + 2x
20y = 18 + 2x
divide all terms by 20:
20y/20 = 18/20 + 2x/20
y = 9/10 + 1/10x
reorder terms for slope intercept form:
y = 1/10x + 9/10
Answer:
[tex]y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]-2x=-20y+18[/tex]
To write the given equation in slope-intercept form, make y the subject.
Add 20y to both sides:
[tex]\implies 20y-2x=-20y+18+20y[/tex]
[tex]\implies 20y-2x=18[/tex]
Add 2x to both sides:
[tex]\implies 20y-2x+2x=2x+18[/tex]
[tex]\implies 20y=2x+18[/tex]
Divide both sides by 20:
[tex]\implies \dfrac{20y}{20}=\dfrac{2x+18}{20}[/tex]
[tex]\implies \dfrac{20y}{20}=\dfrac{2x}{20}+\dfrac{18}{20}[/tex]
[tex]\implies y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]
Therefore, the given equation in slope-intercept form is:
[tex]\boxed{y=\dfrac{1}{10}x+\dfrac{9}{10}}[/tex]
Find the value of z such that 0.03 or f the area lies to the right of z Round your answer tom2 decimal places
ANSWER
z = 1.88
EXPLANATION
We have to find z such that the area under the normal curve to the right of that value is 0.03,
This is the same as finding z such that the area to the left of that value is 1 minus 0.03,
[tex]1-0.03=0.97[/tex]These are the values that z-score tables show. So, we have to find a z-score where the value in the table is 0.97,
The z-score whose area to its left is closest to 0.97 is z = 1.88.
Hence, for z = 1.88, the area under the curve to its right is 0.03.
Choose the correct translation for the following statement.It must exceed seven.Ox<7Ox57Ox>7Ox27
Solution:
Given that a value or quantity must not exceed ten, let x represent the value or quantity.
Since it must not exceed 10, this implies that
[tex]x\leq10[/tex]The second option is the correct answer.
use the following graph to find the mean, median, and mode
Given:
A graph
To determine the Mean, Median, and Mode based on the given graph, we first get the data set as shown below:
2,5,5,5,5,6,9,11,12,13,14,15,18,20
Next, we find the Mean by getting the average:
[tex]\begin{gathered} Mean=\frac{2+5+5+5+5+6+9+11+12+13+14+15+18+20}{14} \\ Simplify \\ Mean=\frac{140}{14} \\ Mean=10 \end{gathered}[/tex]Then, we get the Median by getting the average of the two middle values since there is an even number of data values:
[tex]\begin{gathered} Median=\frac{9+11}{2} \\ Simplify \\ Median=10 \end{gathered}[/tex]Now, we get the Mode by finding the number that appears most frequently. Hence, the Mode is 5.
Therefore, the answer is:
Mean:10, Median:10, Mode:5
ABCD is a parallelogram
BE= 6x+44
ED= -6x-16
Find the length of BD
The line segment BD has a length of 18 units
How to calculate the length of BD?The possible figure is added as an attachment
From the question, we have the following parameters:
Name of shape = ABCDShape type = ParallelogramBE = 6x + 44ED = -6x - 16The lengths BE and ED implies that the point E is between the endpoints B and D
Since the shape is a parallelogram, then the point E is halfway between the endpoints B and D
So, we have
BE = ED
Substitute the known values in the above equation
6x + 44 = -6x - 16
Evaluate the like terms
So, we have
12x = -60
Divide both sides by 12
x = -5
Substitute x = -5 in BE = 6x + 44
So, we have
BE = 6 x -5 + 44
Evaluate
BE = 14
The length is then calculated as
BD = 2 x BE
So, we have
BD = 2 x 14
Evaluate
BD = 18 units
Hence, the length of BD is 18 units
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Help please.
We have the equation negative 9 minus this whole expression, 9x minus 6—this whole thing is being subtracted from negative 9—is equal to 3 times this whole expression, 4x plus 6.
Solve the Equation
The value of x in the equation given is x = -4/7.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The information given will be illustrated as:
9 - (9x - 6) - 9 = 3(4x + 6)
9 - 9x + 6 - 9 = 12x + 18
Collect like terms
-9x + 6 = 12x + 18
-9x - 12x = 18 - 6
-21x = 12
Divide
x = 12/-21
x = -4/7
This illustrates the concept of equations.
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