The fraction 9/10 is more than 78/100.
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that are combined in a meaningful way.
To compare these two fractions, we can convert them to have a common denominator. In this case, the common denominator is 1000.
9/10 = (9/10) x (100/100) = 900/1000
78/100 = (78/100) x (10/10) = 780/1000
Now we can see that 900/1000 (which is equivalent to 9/10) is greater than 780/1000 (which is equivalent to 78/100).
Therefore, 9/10 is more than 78/100.
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Explain whether the research topic is best investigated through an experiment or an observational study. Then describe the design of the experiment or observational study.
1. A cycling team wants to know whether incorporating yoga into a workout routine improves racing times.
2. A researcher wants to compare the effects of a new experimental cancer drug with a cancer drug that has been used for at least 10 years.
Find the measure of angle AEF in regular hexagon ABCDEF.
Answer:
30°
Step-by-step explanation:
You want the measure of angle AEF in regular hexagon ABCDEF.
Interior anglesThe interior angles of a regular hexagon are ...
180° -(360°/6) = 120°
Angle AEF is 90° less than this, so is ...
angle AEF = 120° -90°
angle AEF = 30°
__
Additional comment
Angle AEF is also a base angle of isosceles triangle AEF, which has angle F = 120°. The base angles are (180° -120°)/2 = 30°.
Number of hours at work
Graduates Non-graduates
9641 2138
6655432 3 13445559
93310 4 346889
92501
(a) What were the ranges for the two groups?
hours
Graduates
Non-graduates
hours
(b) Which group had more responses in the 40s?
O Graduates O Non-graduates O Each had the same
(c) Which group had the greater median number of hours?
O Graduates O Non-graduates O The medians were the same
(a) The range for the graduates is 86760 hours.
(c) The graduates had the greater median number of hours.
(a) The range is the difference between the maximum and minimum values in a set of data. We are given the following data:
Graduates: 9641 hours, 6655432 hours, 93310 hours, and 92501 hours
Non-graduates: 2138 hours, 3 hours, 4 hours, and 13445559 hours
The range for the graduates is 9641 - 92501 = 86760 hours.
The range for the non-graduates is 2138 - 13445559 = 13443421 hours.
(c) To find the median, we need to arrange the data in order from smallest to largest and find the middle value. If there are an even number of data points, we take the average of the two middle values.
Graduates: 9641 hours, 93310 hours, 92501 hours, 6655432 hours
The median is the average of 93310 hours and 92501 hours, which is (93310 + 92501)/2 = 92905.5 hours.
Non-graduates: 2138 hours, 3 hours, 4 hours, 13445559 hours
The median is the average of 3 hours and 4 hours, which is (3 + 4)/2 = 3.5 hours.
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The sum of two numbers is 5 the product of the same two numbers is 20
The two numbers are 4 and 1.
What are the two numbers?To solve the problem, we will use algebraic equations.
We will call 2 numbers x and y. So, we know that:
------ x + y = 5 (equation 1)
------ xy = 20 (equation 2)
We will solve for y in terms of x:
y = 5 - x
We will substitute for y into equation 2 and simplify:
x(5 - x) = 20
5x - x^2 = 20
x^2 - 5x + 20 = 0
As a quadratic equation which will be solved using the quadratic formula, the solutions are x = 4 and x = 1. We can check that these solutions satisfy both equation 1 and equation 2.
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please help quickly
Answer: B
Step-by-step explanation:
First, you have to know that a straight line is equal to 180 degrees. They gave you 115 degrees in part of a line, so the other part or the angle not given must be equal to 65 degrees. Another thing is that a triangle has 180 degrees. 65+80 degrees is equal to 145 degrees, leaving angle 1 to be equal to 35 degrees. Another thing to know is that reflective angles have the same measurement. If the original angle was equal to 65 after subtraction 115 from 180, we know that the second triangle's angle would also be equal to 65. 65+86 is 150, and 180-150 is 30. Thus, the answer is B.
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Triangle ABC ~ triangle DEF.
triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 2.2
Brainliest for right answer!!!!
Will give Brainliest and points!!!!
Determine the measurement of FD.
FD = 1.52
FD = 1.58
FD = 1.1
FD = 5.5
Answer:
The answer is **FD = 1.52**.
Since triangle ABC ~ triangle DEF, we know that the ratio of their corresponding sides is equal. So, we have:
```
AB/DE = AC/DF = BC/EF
```
We are given that AB = 11, DE = 2.2, and AC = 7.6. Substituting these values into the first equation, we get:
```
11/2.2 = 7.6/DF
```
Cross multiplying, we get:
```
11 * DF = 2.2 * 7.6
```
```
DF = (2.2 * 7.6) / 11
```
```
DF = 1.52
```
Step-by-step explanation:
CRITICAL THINKING The total area of the polygon is 176 square feet. What is the value of $x$ ?
A drawing of a polygon. It consists of a rectangle with two triangles on either side. Length of the rectangle is 16 feet. The width of the rectangle is 8 feet and is same as the height of the triangles. Lengths of the base of each triangle is labeled as x.
$x=$
ft
The value of x is, x = 6 ft
Now, We can formulate;
Area of the polygon = area of the square + 2(area of the triangle)
Here, We have;
Area of the polygon = 176 ft²
So, Area of the square = length × width
= 16 × 8
= 128
And, Area of the two triangles = 2( 1/2 x base x height)
= 2(1/2 × x × 8)
= 8x
Now, Plug in the above values into the equation for area of the polygon.
Thus: We get;
176 = 128 + 8x
Subtract 128 from each side
176 - 128 = 8x
48 = 8x
Divide both sides by 8
6 = x
x = 6 ft
Thus, The value of x is, x = 6 ft
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Andrew is making fresh lemonade. If he needs 3 lemons to make one glass of lemonade, how many glasses can he make with 28 lemons?
Answer:
he can make 9 cups of lemonade and he will have 1/3 of a cup of lemonade left over
Step-by-step explanation:
28÷3=9.3333=28/3=9 1/3
Answer:
9.3 or just 9 glasses of lemonade in total.
Step-by-step explanation:
just divide 28 with 3. but just to round it up i would say 9 glasses of lemonade.
2. Find the length of MN in the triangle below. M A. 2√23 B. 3√13 C. 4√6 D. 8√2
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{24}\\ a=\stackrel{adjacent}{22}\\ o=\stackrel{opposite}{MN} \end{cases} \\\\\\ MN=\sqrt{ 24^2 - 22^2} \implies MN=\sqrt{ 92 }\implies MN=2\sqrt{23}[/tex]
Lin is using technology to create a segmented bar graph from a spreadsheet and is following the steps listed. What is the missing step?
Step 1. Copy your relative frequency table into the spreadsheet.
Step 2: ?
Step 3: Highlight the data of the relative frequency table.
Step 4: Insert the proper type of graph using the “Insert” tab.
Step 5: Check the elements of the graph to ensure the appearance is correct.
ANSWER CHOICES
A.convert your data into percentages.
B. Total the columns.
C. Add a title to the graph.
D. Label each row and column.
Note the the missing step is: " Total the columns." (Option B) so the completed step with regard to the segmented bar graph is given below.
What is a segmented bar graph?A segmented bar chart uses vertical or horizontal bars to compare two or more categories. Typically, the stacked bars represent each group's percentage of the whole and are plotted by the proportion of each value inside each group.
This style of chart can be beneficial for comparing total amounts across each split bar or group. It may be an effective method of forecasting a company's profit over a period of months, with the earnings separated into distinct product lines.
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Penn volunteered a total of 96 hours
over the last 12 weeks. He
volunteered the same number of
hours each week.
How many hours did Penn volunteer
in one week? Write an equation
and solve the problem.
Equation:
Answer:
The number of hours Penn volunteer in one week is 8hours
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
Representing the number of hours volunteered in a week by Penn by x
therefore for 12 weeks , the number of hour will be;
12×x = 12x
12x = 96
divide both sides by 12
x = 96/12 = 8 hours
therefore the number of hour volunteered by Penn in a week is 8 hours
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Tell whether the ordered pair is a solution of the equation
Y=6x; (0,3)
Answer:
Yeeeaaa, no.
Hope this helps!
Step-by-step explanation:
( x, y )
Plug the numbers of the ordered pair into the equation: y = 6x
3 = 6 × ( 0 )
3 = 0
Three does not equal zero...
3 [tex]\neq[/tex] 0
The length of a rectangle is 3 inches longer than its width. If the area is 154 square inches, what are the dimensions of the rectangle
Step-by-step explanation:
Draw a rectangle. If the length is 3 inches longer than its width, we can write the width as "w" and the length as the width + 3
Area is (width)(Length) = (width)(width+3)
W
----------
| |
| |
| | L = w+3
| |
| |
-----------
A = (w+3)(w)
A = w2 + 3w = 108.
(Problem states that area is 108 sq in)
Need to solve this quadratic equation
w2 + 3y - 108 = 0
Factor:
(w - 9) (w + 12) = 0
So
w - 9 = 0. or. w + 12 = 0
Solve these and get
w = 9. or. w = -12
Only one that makes sense in real life is the poitive one.
So the dimensions are
Width = 9 inches
Length = 12 inches
hope this helped-nia.
the rectangular wall measures 14 ft by 12 feet. Each square foot of wallpaper costs 2.90. Find the cost of covering the wall with paper?
Answer:
487.20
Step-by-step explanation:
1. find the area of a rectangle ( length x width)
14ft x 12ft = 168ft²
2. Multiply the number of feet needed to becovered by the price of one foot of paper
168ft x 2.90 = 487.20
Geomerty Math PLSSS ANSWER
Answer: first do multiplcation for each part then add everythink to find total volume
Step-by-step explanation:
Need help please !! And I need an explanation too
He covered a distance of 5 miles for 5 days of the total days of training. The total distance he covered = 6 miles.
How to calculate the distance covered by Anthony during his training?The total number of days Anthony used for training = 8 days.
The number of days he covered 1/4 mile = 2days
The number of days he covered 1/2 mile = 1 day
The number of days he covered 1 mile = 5 days.
Therefore that total distance that he used for the training = 2(1/4)+1(1/2)+5(1)
= 0.5+0.5+5
= 6 miles.
The number of days he covered the highest distance would be for 5 days.
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HELP I NEED TO TURN THIS IN IN 10 MINUTES!!
The doubling period of a bacterial population is 15 minutes. At time t=110 minutes, the bacterial population was 70000
What was the initial population at time t=0?
Find the side of the bacterial population after 5 hours
Answer:
Step-by-step explanation:
1. the initial population at t=0 is 1
2. 16
It costs a car company $25,000,000 to develop and market the model of a new car. The company sells each car for $30,000 . Which of the following represents the number of cars, c , that the car company must sell to make over $5,000,000 in profit?
Answer: so if it cosst 25,000,000 dollars to market a car and they sell it for 30,000 dollars they would need to sell 167 cars to get 5.1 million dollars or 166 for 5.0 million
show that the solution to the differential equation dp/dt=-0.1P is P=495e^1.1t
We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).
We have,
To show that the solution to the differential equation dp/dt = -0.1P is
P = 495e^(1.1t),
we can use separation of variables and integration.
Starting with the differential equation:
dp/dt = -0.1P
We can separate the variables by dividing both sides by P and multiplying both sides by dt:
dp/P = -0.1 dt
Integrate both sides:
∫ dp/P = -0.1 ∫ dt
Integrating the left-hand sid.
ln|P| = -0.1t + C
where C is the constant of integration.
To solve for C, we can use an initial condition.
Suppose that when t = 0, P = P0.
Then we have:
ln|P0| = -0.1(0) + C
ln|P0| = C
Substituting this value of C back into the equation for P.
ln|P| = -0.1t + ln|P0|
ln|P/P0| = -0.1t
Taking the exponential of both sides.
P/P0 = e^(-0.1t)
Multiplying both sides by P0.
P = P0 e^(-0.1t)
We can substitute P0 = 495 (since P(0) = 495 is given in the solution) and e^(-0.1t) = e^(1.1t)/e^t.
P = 495 e^(1.1t)/e^t
Simplifying the expression by combining the exponentials.
P = 495 e^(0.1t)
which is the same as the given solution.
Therefore,
We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).
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How do I solve the problem using substitutions?
By using the substitution method, the value for (x,y) = (-2, 2)
What is the substitution method in algebra?The substitution method for solving a system of algebra equations is a process where by we make a variable (say variable x) the subject of the formula and substitute it into the second equation to solve for the other variable.
In essence, from the given system of equations; let's make x the subject of the formula in the first equation.
5x + 3y = -4
5x = -4 - 3y
Divide both sides by 5;
x = -4/5 - 3y/5
Now, we are going to substitute this value for x into the second equation. The second equation says:
y - 2x = 6
y - 2(-4/5 - (3y/5)) = 6
By solving for y;
y = 2
Now, let's replace the value of y with any of the given equation (2);
y - 2x = 6
2 - 2x = 6
-2x = 6 - 2
-2x = 4
Divide both sides by -2
-2x/-2 = 4/ -2
x = -2
Therefore, we can conclude that by using the substitution method, the value for (x,y) = (-2, 2)
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I need help ASAP!!
The length of a rectangle is 4 meters longer than its width.
The area of the rectangle is
117m^2.
What is the width of the rectangle?
HINT: you can use DESMOS for this kind of problem.
Answer:
w(w + 4) = 117
w^2 + 4w = 117
w^2 + 4w - 117 = 0
(w - 9)(w + 13) = 0
w = 9 meters
The width of the rectangle is 9 meters, and the length of the rectangle is 13 meters.
15 POINTS!!!!! HELP DUE IN 10 MINS!!!!!!!!!
Use the graph to answer the question.
Determine the line of reflection.
Reflection across the x-axis
Reflection across x = −6
Reflection across the y-axis
Reflection across y = −6
A line of reflection, also known as a line of symmetry, is a line that divides a figure into two congruent parts that are mirror images of each other.
When a figure is reflected across a line of reflection, every point on one side of the line has a corresponding point on the other side of the line that is equidistant from the line.
To determine the line of reflection for the given graph:
- Reflection across the x-axis: The line of reflection is the x-axis.
- Reflection across x = -6: The line of reflection is a vertical line passing through x = -6.
- Reflection across the y-axis: The line of reflection is the y-axis.
- Reflection across y = -6: The line of reflection is a horizontal line passing through y = -6.
Thus, the line of reflection is the perpendicular bisector of every segment joining a point to its image after reflection.
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Can someone please tell me what's the answer to convert 35 deca to km and m. my school is about to start
Answer:
1km:100decameter(dam)
Step-by-step explanation:
so 35dam:0.35km
and 35dam:0.00035m
solve: 63+48÷(23-11)×14
Answer:
119
Step-by-step explanation:
Firstly, we need to solve the expression inside the parentheses, which is 23-11. This gives us 12. Then we need to carry out the division to get 48 divided by 12, which is 4. We can then multiply 4 by 14 to get 56. Finally, we add 56 to 63 which gives us the answer of 119. Therefore, the solution to the expression 63+48÷(23-11)×14 is 119.
Question 25 of 40
The linearized regression equation for an exponential data set is log ý = 0.14x
+0.4, where x is the number of years and y is the population.
What is the predicted population when x = 20? Round your answer to the
nearest whole number.
A. 112,590
B. 1585
C. 630
D. 3
Answer:c
Step-by-step explanation:
Answer: B 1585
took the test
The product of two numbers is 126 . The smaller number is 5 less than the larger number. Which of the following equations can be used to solve for the larger number?
Answer:
Step-by-step explanation:
45
how to solve for the below problems
The Taylor polynomial of degree 3 for sin(x) for x near 0 is,
sin (x) = x - 1/6 x³
The ratio is sin (x) / x = 1 - 1/6 x².
Limit is 1.
Given function is sin(x).
We have to find the Taylor Polynomial for sin (x).
We know that,
f(x) = sin(x), so f(0) = sin (0) = 0
f'(x) = cos (x), so f'(0) = cos (0) = 1
f''(x) = -sin (x), so f''(0) = sin (0) = 0
f³(x) = -cos (x), so f³(0) = -cos(0) = -1
Taylor polynomial is,
sin (x) = {[f(0) (x - k)⁰] / 0!} + {[f'(0) (x - k)¹] / 1!} + {[f''(0) (x - k)²] / 2!} + {[f³(0) (x - k)³] / 3!}
Here c = 0.
sin (x) = 0 + x + 0 + (-x³/6)
sin (x) = x - 1/6 x³
The ratio,
sin (x) / x = (x - 1/6 x³) / x = 1 - 1/6 x²
When x tends to 0 in the expression, 1 - 1/6 x², the value tends to 1 - 0 = 1.
Hence the required Taylor polynomial is sin (x) = x - 1/6 x³.
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Find the volume of the shape below. Round to the nearest tenth. Use
the pi button on the calculator.
12 ft
Volume=
4 ft
ft3
The volume of the cone with a diameter of 4ft and height 12ft is approximatelly 50.3 ft³
What is the volume of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The volume of a cone is expressed as;
V = (1/3)πr²h
The figure in the image is a cone.
Diameter of the base of the cone d = 4ft
Radius r = diameter/2 = 4/2 = 2ft
Height h = 12ft
Plug the given values into the above formula and solbr for the volume.
V = (1/3)πr²h
V = (1/3) × π × r² × h
V = (1/3) × π × (2 ft )² × 12ft
V = 50.3 ft³
Therefore, the volume is 50.3 ft³.
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Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
The coordinates of the vertices for the image if the preimage is translated 3 units up is : A′(−3, 6), B′(0, 10), C′(−3, 3).
The correct option is (B)
Translations:If we are given the translated image of something, we need to work backwards given the translation rules. For example, if we have a general translation of (x +a, y +b), then to find pre-translation coordinates, we do: (x−a, y−b).
We have the Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0).
Now, let's consider the translation that moves the triangle 3 units up. This means that we need to add 3 to the y-coordinate of each vertex to get the coordinates of the image.
So, the coordinates of the vertices of the image triangle, let's call it A'B'C', will be:
A' = (-3, 3+3) = (-3, 6)
B' = (0, 7+3) = (0, 10)
C' = (-3, 0+3) = (-3, 3)
The coordinates of the vertices for the image if the preimage is translated 3 units up is : A′(−3, 6), B′(0, 10), C′(−3, 3)
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how to solve the power series below
The first five coefficients are explained.
Given is power series, f(x) = eˣ about x = 4 as [tex]\sum_{\infty}^{n=0}C_n}(x+4)^n[/tex]
f(x) = eˣ
a = 4,
The general form of a Taylor series is:
f(x) = [tex]\sum_{n=0}^{\infty}\frac{f'(a)}{n!} (x-a)^n[/tex]
Note that since the function is a basic exponential function, its derivative is:
f'(x) = eˣ
That is, the function is the same for whatever order of differentiation. So, let us substitute our values here,
f(x) = [tex]\sum_{n=0}^{\infty}\frac{e^4}{n!} (x-4)^n[/tex]
The general expression for the coefficients is: [tex]C_n = \frac{e^4}{n!}[/tex]
The first coefficient is: [tex]C_0 = e^4[/tex]
The second coefficient is: [tex]C_1 = e^4[/tex]
The third coefficient is: [tex]C_2 = 1/2e^4[/tex]
The fourth coefficient is: [tex]C_3 = 1/6e^4[/tex]
And lastly,
[tex]C_4 = 1/24e^4[/tex]
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