Answer:
150 minutes
Step-by-step explanation:
Since your solving for minutes you need to change the 2.5 hours into minutes. There is 60 minutes in 1 hour. you take 60 and multiply it by 2.5 because you need to find the total minutes. When you multiply those teo you get 150 minutes. Please give me the brainliest answer.
:D Hoped this helped!!! Have a good day!! <3
Answer:
150 minutes
Step-by-step explanation:
1 hours = 60 minutes
We need to use the conversion factor with minutes on top
2.5 hours * 60 minutes
-------------
1 hour
Canceling hours
2.5 *60 minutes
150 minutes
Five friends share 3 bags of trail mix equally. What fraction of a bag of trail mix does each friend get? Please explain or show your work! :)
Each friend should get 1/5 of a bag of trail mix. Since there are three bags of trail mix, you would add those into it. Hope this helps!
In quadrilateral ABCD the measures of, A , B , C, and D are the ratio of 1 :2:3:4, respectively. Find the measures of the four angles
So the ratio are 1:2:3:4 and all these add up to 10
Now we divide 360 by 10 resulting to 36
A=(36)
B=(72)
C=(108)
D=(144)
All these add up to 360 and has been divided equally according to the ration provided
Final answer:
To find the measures of the angles in quadrilateral ABCD with ratios 1:2:3:4, we set the angles as x, 2x, 3x, and 4x, and use the fact that their sum equals 360 degrees. Solving for x, we find x to be 36 degrees, which gives us the individual angles as 36 degrees, 72 degrees, 108 degrees, and 144 degrees respectively.
Explanation:
Calculating the Measures of the Angles in a Quadrilateral
Given that the measures of the angles A, B, C, and D in quadrilateral ABCD are in the ratio of 1:2:3:4 respectively, we first need to understand that the sum of the interior angles in a quadrilateral is always 360 degrees. To find the measure of each angle, we should express the ratio in terms of x, which would give us the angles as x, 2x, 3x, and 4x. Summing these and setting them equal to 360 degrees, we get the equation x + 2x + 3x + 4x = 360. Simplifying, we have 10x = 360, which when solved for x yields x = 36 degrees. Therefore, the measures of the angles are:
Angle A = 1x = 36 degrees
Angle B = 2x = 72 degrees
Angle C = 3x = 108 degrees
Angle D = 4x = 144 degrees
Hence, each angle's measure has been found using the given ratio and the property of the sum of interior angles in a quadrilateral.
A group of friends go to a local fair. Jason spends $3.75. My has spent three times as much as Jason. Tia spend $5.25 more than Maya how much money how much does Tia spend.
Answer:
$16.50
Step-by-step explanation:
If Jason spends $3.75 and Maya spends three times that amount, Maya spends 3.75(3) or $11.25. If Tia spends $5.25 more than Maya, Tia spends 11.25 + 5.25 or $16.50.
Maggie buys 4 shirts that are the same but in different colors.The total cost for all 4 shirts before sale tax is 85.80 if all 4 shirts the same price how much does 1 cost
Condense the following log into a single log:
[tex]log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z[/tex]
Answer:
[tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]
Step-by-step explanation:
Given in the question an expression
[tex]log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z[/tex]
To Condense this log into a single log we will use logarithm rules
1)Power rulelogb(x^y) = y ∙ logb(x)
[tex]\frac{1}3}log_{3} y = log_{3}y^\frac{1}{3}[/tex]
[tex]5log_{3} z = log_{3} z^5[/tex]
2)Product rulelogb(x ∙ y) = logb(x) + logb(y)
[tex]log_{3} x + log_{3}y^\frac{1}{3} = log_{3}(x . y^\frac{1}{3} )[/tex]
3)qoutient rule[tex]logb(x / y) = logb(x) - logb(y)\\log_{3}(x . y^\frac{1}{3} )- log_{3} z^5[/tex]
= [tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]
Find the value of the lesser root of x2 - 8x + 7 = 0.
A) -1
B) 1
C) 3
D) 5
Answer:
B) 1.
Step-by-step explanation:
x^2 - 8x + 7 = 0
(x - 1)(x - 7) = 0
x= 1, 7.
Answer:
x = 1
Step-by-step explanation:
Please express exponentiation using the symbol " ^ " : x^2 - 8x + 7 = 0
Let's solve this equations using "completing the square:"
x^2 - 8x + 7 = 0
1) Identify the coefficient of the x term. Here it's -8.
2) take half of that and square it: we get (-4)² = 16
3) insert " +16 - 16 " between the 8x and the 7:
x^2 - 8x + 16 - 16 +7 = 0
4) Rewrite this perfect square:
(x - 4)² - 16 + 7 = 0 -> (x - 4)^2 = 9
5) Solve for (x -4) by taking the square root of both sides:
x - 4 ± sqrt(9) -> x - 4 ± 3
6) Solve for x: x = 4 ± 3, or x = 7 and x = 1.
7) Take the lesser root of 7 and 1. That would be x = 1. Answer B is correct.
1. Find the missing side length. Round your answer to the nearest tenth.
6.7 21.3 5.5 43.2
2. Find the length of side a. Round to the nearest tenth.
12 378.4 18.3 19.5
3. Find the length of side BA. Round to the nearest hundredth.
0.42 0.65 0.83 1.25
QUESTION 1
We can use the cosine rule to find the missing side length.
Recall that the cosine rule for a triangle with sides a,b,c and an included angle A is
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
Let the missing side length in the triangle with sides 6, 9 and the included angle of [tex]37\degree[/tex] be [tex]a[/tex] units.
We then substitute the values into the cosine rule to obtain;
[tex]a^2=6^2+9^2-2(6)(9)\cos 37\degree[/tex]
[tex]a^2=36+81-108\cos 37\degree[/tex]
[tex]a^2=30.747[/tex]
[tex]\Rightarrow a=\sqrt{30.747}[/tex]
[tex]\Rightarrow a=\sqrt{30.747}[/tex]
[tex]\Rightarrow a=5.5[/tex] units to the nearest tenth.
QUESTION 2
We again use the cosine rule: [tex]a^2=b^2+c^2-2bc\cos A[/tex]
We substitute the given values to obtain;
[tex]a^2=11^2+13^2-2(11)(13)\cos 108\degree[/tex]
[tex]a^2=121+169-286\cos 108\degree[/tex]
[tex]a^2=378.379[/tex]
[tex]\Rightarrow a=\sqrt{378.379}[/tex]
[tex]\Rightarrow a=19.5[/tex] to the nearest tenth
QUESTION 3
We again use the cosine rule :
[tex]|BA|^2=(\frac{1}{2})^2+(\frac{1}{3})^2-2(\frac{1}{2})(\frac{1}{3})\cos 100\degree[/tex]
[tex]|BA|^2=0.418899[/tex]
[tex]|BA|=\sqrt{0.418899}[/tex]
[tex]|BA|=0.65[/tex] to the nearest hundredth
Solve for x. -7/8x = -5
Answer:4.375 Maybe?
Step-by-step explanation:
In a sofa store 30% of the sofas are leather. 40% of the leather sofas are black. What percentage of the total number of sofas are made form black leather?
Answer:
12%
Step-by-step explanation:
Given,
% of leather sofas = p(A) = 30% = 30/100 = 0.3
% of leather sofas that are black = p(B) = 40% = 40/100 = 0.4
The percentage of total sofas made from leather = p(A) * p(B)
= 0.3 * 0.4
= .12
= 12%
If a point a is located at 2/3 and there are 10 points between A and B what could be the possible coordinates for point B
The possible coordinates for point B that are 10 units away from point A at (2,-3) could be (12, -3), (2, 7), (-8, -3), or (2, -13), moving directly horizontal or vertical.
If point A is located at (2,-3), and there are 10 points between A and B, we're likely looking at points equidistant from A, forming a sort of 'circle' with A at the centre. However, in a Cartesian plane, if the distance between two points is equal to 10 units, there are various possibilities depending on the orientation of the line connecting the two points.
For a point B to be 10 units away from point A at (2, -3), it can move horizontally to the right or left, or vertically up or down. Thus, the possible coordinates for point B would change by 10 units either in the x-coordinate (horizontally) or the y-coordinate (vertically).
Possible Coordinates for Point B
Horizontally to the right: (2+10, -3) = (12, -3)
Vertically up: (2, -3+10) = (2, 7)
Horizontally to the left: (2-10, -3) = (-8, -3)
Vertically down: (2, -3-10) = (2, -13)
Other options like (12, -6), (2, -7), (12, 3), or (-8, 3) do not adhere to being 10 units away from point A directly horizontally or vertically.
The complete question is:
If point A is located at (2,-3) , and there are 10 points between A and B, what * 1 could be the possible coordinates for point B? Choose all that apply. (12,-3) (2,7) (12,-6) (-8,-3) (2,-7) (-8,3) (2,-13) (12,3)
A rectangular price tag has an area of 36 square centimeters. Its perimeter is 26 centimeters. What are the dimensions of the price tag?
Final answer:
The dimensions of the price tag are 9 cm by 4 cm, which are found by solving two equations derived from the given area and perimeter.
Explanation:
The student is asking for the dimensions of a rectangular price tag that has an area of 36 square centimeters and a perimeter of 26 centimeters. To solve this, we need to use two formulas: one for area (A = length × width) and one for perimeter (P = 2 × (length + width)).
First, let's denote the length of the rectangle by l and the width by w. The given area, 36 cm2, implies that l × w = 36.
Second, we know the perimeter is 26 cm, which gives us the equation 2 × (l + w) = 26. Dividing both sides by 2, we get l + w = 13.
This system of equations can be solved using substitution or elimination. If we rearrange the perimeter equation to express one variable in terms of the other (for instance, w = 13 - l), we can then substitute this expression into the area equation. Solving for l and w afterwards will give us the required dimensions.
Through solving, we find that the dimensions of the rectangle are 9 cm by 4 cm, since 9 × 4 = 36 and 2(9 + 4) = 26.
What is the value of x? Enter your answer in the box.
Check the picture below.
notice, we use the 30-60-90 rule to get the length of RT, and then the 45-45-90 rule to get "x".
Answer:
Step-by-step explanation:
Remark
x is going to be the same thing as the hypotenuse of ΔRST. Find that and you have x.
Givens
<STR = 60°
RT = 2√3
Solution
Sin(60°) = opposite / hypotenuse
Sin(60°) = √3 / 2
Sin (60°)= 2 √3 / hypotenuse
hypotenuse = 2√3 // sin(60°)
hypoteneuse = 2√3 /√3/2
[tex]\text{hypotenuse = }\dfrac{2\sqrt{3}}{\dfrac{\sqrt{3} }{2}} = 2*2[/tex]
The √3's cancel. The answer is 4
========================
ΔRTQ is a right angle isosceles triangle
∴RT = RQ
X = 4
Jessie's daughter went to Target and bought $1 or $2 items from the One Spot area. She wants to spend less than $20 at Target
She can buy 20 1$ items, or 10 $2 items, at most
At a doctor's appointment, a baby weighed 10 pounds. How many ounces did the baby weigh?
Answer:
The baby would be 160 ounces.
Step-by-step explanation:
The baby who weighted 10 pounds, weighs 160 ounces.
How to convert a weight from pound to ounces ?Given that at a doctor's appointment, a baby weighed 10 pounds.
From the conversion table, we know that 1 pound is equal to 16 ounces.
Thus 10 pounds is equal to 160 ounces.
Therefore, the baby weighted 160 ounces.
To learn more about conversion of units, refer -
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The length of a rectangle is four times its width. If the area of the rectangle is 100 ft?, find its perimeter
The width of the rectangle is 5 feet, its length is 20 feet. Thus, the perimeter is 50 feet.
To solve this problem, let's denote:
- Width of the rectangle as w (in feet)
- Length of the rectangle as 4w (since it's four times the width)
Given that the area of the rectangle is 100 square feet, we can set up the equation for the area:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
[tex]\[ 100 = (4w) \times w \][/tex]
[tex]\[ 100 = 4w^2 \][/tex]
Now, let's solve for ( w ):
[tex]\[ 4w^2 = 100 \][/tex]
Divide both sides by 4:
[tex]\[ w^2 = 25 \][/tex]
Taking the square root of both sides:
[tex]\[ w = \sqrt{25} \][/tex]
[ w = 5 ]
So, the width of the rectangle is ( w = 5 ) feet.
Now, we can find the length:
[tex]\[ \text{Length} = 4w = 4(5) = 20 \] feet.[/tex]
Now that we have both the width and length, we can find the perimeter of the rectangle using the formula for perimeter:
[tex]\[ \text{Perimeter} = 2(\text{Length}) + 2(\text{Width}) \][/tex]
[tex]\[ \text{Perimeter} = 2(20) + 2(5) \][/tex]
[tex]\[ \text{Perimeter} = 40 + 10 \][/tex]
[tex]\[ \text{Perimeter} = 50 \][/tex]
So, the perimeter of the rectangle is ( 50 ) feet.
Determine whether the given equation has one solution, no solution, or infinitely many solutions: 4x+10=2(2x+5)
if we distribute 2(2x+5), we'll end up with 4x + 10, so in short, the right-hand-side, is really the left-hand-side in disguise.
and since 4x + 10 = 4x + 10, both equations are equal, meaning in short, the system has an infinite number of solutions.
What is m∠A ? Can someone help me
Answer:
38°
Step-by-step explanation:
The triangle solver app on your calculator, phone, or tablet can solve this for you readily. There are on-line triangle solvers, too.
___
For solution "by hand", the Law of Cosines is useful. It tells you ...
a^2 = b^2 + c^2 -2ab·cos(A)
Then the angle A can be found as ...
cos(A) = (b^2 +c^2 -a^2)/(2ab) = (3^2 +7^2 -5^2)/(2·3·7) = 33/42 = 11/14
A = arccos(11/14) ≈ 38°
_____
In formulas like the Law of Cosines or the Law of Sines, the uppercase letters stand for the measures of angles, and the lowercase letters stand for their opposite side lengths.
Bernie wants to write equations in the form y=mx+b for the lines passing through point P that are parallel and perpendicular to line r. First he finds the slopes of these two lines. What could he do next to find the y-intercepts?
Answer:
Substitute the slope and the coordinates of point P in the equation of the line y=mx+b and then solve for b in each equation
Step-by-step explanation:
we know that
The first step is calculate the slopes of these two lines. Remember that if two lines are parallel then the slopes are the same (m1=m2) and if two lines are perpendicular then the slopes is equal to m1*m2=-1
The second step is substitute the slope m2 and the coordinates of point P in the equation of the line in slope-intercept form y=mx+b and then solve for b in each equation
Answer:
Step-by-step explanation: See answer below
When b= 0.5, the period of orange graph is _ pi
When b= 2, the period of orange graph is _ pi
Answer:
When b= 0.5, the period of orange graph is _4_ pi
When b= 2, the period of orange graph is _1_pi
Step-by-step explanation:
The period of the sinusoidal functions can be easily calculated by observing their graphs.
First, look at the orange graph when b = 0.5
Identify a point where the orange chart cuts the x-axis. For example at [tex]x = 0[/tex]. After completing the rise and fall cycle, the function cuts back to the x axis at [tex]x = 4\pi[/tex].
Then the period [tex]T = 4\pi[/tex].
Second, look at the orange graph when b = 2
Identify a point where the orange chart cuts the x-axis. For example at [tex]x = 0[/tex]. After completing the rise and fall cycle, the function cuts back to the x-axis at [tex]x = \pi[/tex].
Then the period [tex]T = \pi[/tex].
We also know that the period of a sinusoidal function is defined as [tex]T(b) = \frac{2\pi}{b}[/tex]
So:
[tex]T(0.5) = \frac{2\pi}{0.5} = 4\pi\\\\T(2) = \frac{2\pi}{2} = \pi[/tex]
Answer:
Part 2:
Based on this evidence,
When b > 1, the period
✔ decreases
.
When 0 < b < 1, the period
✔ increases
Step-by-step explanation:
This is correct for edge 2020. Hope this helps someone.
You got a job selling books at the mall. You are paid $70 per day plus $2 for each book you sell. Which recursive formula models this situation?
Answer:
f(x) = 70 + 2x
Step-by-step explanation:
In this problem, we first need to consider how much we get per day.
$70 is our constant.
$2 will be dependent on the number of books sold.
Here 'x' will represent the number of books sold.
f(x) = 70 + 2x
Now let's try it out.
Let's say we sold 0 books
f(0) = 70 + 2(0) = 70
This shows us that we only get our constant pay.
Now let's try for 1 or more books.
f(1) = 70 + 2(1) = 72
f(2) = 70 + 2(2) = 74
So the recursive formula f(x) = 70 + 2x is a good formula to model the situation.
Answer:
a1 = 70
an = an–1 + 2
Step-by-step explanation:
Suppose the radius of a circle is 8\color{purple}{8} 8 start color purple, 8, end color purple units. What is its circumference?
The number [tex] \pi [/tex] is defined as the ratio between the circumference and the diameter of a circle. In other words, for every circle, we have
[tex]\pi=\dfrac{C}{d}=\dfrac{C}{2r}[/tex]
Since the diameter is twice the radius.
Solving for the circumference, we have
[tex]C=2\pi r[/tex]
So, in your case, the answer is
[tex]C=16\pi[/tex]
Answer:
50.24
Step-by-step explanation:
Formula = 2πr2 × 3.14 = 6.286.28 × r (8) = 50.24to the nearest thousandth what is the cosine of the angle formed by the line whose equation is y=2x and the positive x axis
The cosine of the angle formed by the line whose equation is y=2x and the positive x axis cos =63.435 to the nearest thousandth
What is meant by angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. The term angle is derived from the Latin word angulus, which means "corner." An angle is the difference in direction between two lines or surfaces. Angles are expressed in degrees.From a common point, the two hands draw different sets of lines. Angle refers to these groups of lines that originate from a common point. Every minute, the two hands form different angles. In real life, an example of an angle is a clock.To learn more about angle, refer to:
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Final answer:
To find the cosine of the angle formed by the line y=2x and the positive x-axis, we calculate the arctangent of the slope (2), which gives us an angle of approximately 63.435 degrees. The cosine of this angle is then approximately 0.447 to the nearest thousandth.
Explanation:
The question is asking for the cosine of the angle formed between the line y = 2x and the positive x-axis. To find this, we first need to determine the angle that the line makes with the x-axis. The slope of the line, given by m, is 2, which also represents the tangent of the angle the line forms with the x-axis (tan(θ) = m). We can calculate the angle using the arctangent function (tan⁻¹).
θ = tan⁻¹(2) = Approx. 63.435 degrees
The cosine of this angle can be found using the cosine function:
cos(θ) = cos(63.435 degrees) = Approx. 0.447
To the nearest thousandth, the cosine of the angle is 0.447.
Help which expression represents the phrase 8 less than the product of 6 and a number x
Answer:
8 < 6x
Step-by-step explanation:
Just write what you see by the letters
Solve the equation (linear equation)
[tex](\frac{16}{9}) ^{2x +5} =(\frac{3}{4})^{x-7}[/tex]
Answer: [tex]x=-\frac{3}{5}[/tex]
Step-by-step explanation:
By the negative exponent rule, you have that:
[tex](\frac{1}{a})^n=a^{-n}[/tex]
By the exponents properties, you know that:
[tex](m^n)^l=m^{(nl)}[/tex]
You can rewrite 16 and 9 as following:
16=4²
9=3²
Therefore, you can rewrite the left side of the equation has following:
[tex](\frac{4^2}{3^2})^{(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3^2}{4^2})^{-(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3}{4})^{-2(2x+5)}=(\frac{3}{4})^{(x-7)}[/tex]
As the base are equal, then:
[tex]-2(2x+5)=x-7[/tex]
Solve for x:
[tex]-2(2x+5)=x-7\\-4x-10=x-7\\-4x-x=-7+10\\-5x=3\\x=-\frac{3}{5}[/tex]
The lengths of plate glass parts are measured to the nearest tenth of a millimeter. The lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.8. Determine the mean and variance of the lengths. (a) mean (in tenths of millimeters) Round your answer to two decimal places (e.g. 98.76). (b) variance (in tenths of millimeters2) Round your answer to three decimal places (e.g. 98.765). (a)
Answer:
A) μ = 590.45 mm; B) σ² = 0.053 mm
Step-by-step explanation:
To find the mean, we add together all of the values and divide by the number of data values:
590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6
There are 8 data values; this gives us
4723.6/8 = 590.45
To find the variance, we subtract each of the data values from the mean. We then square this difference, and find the mean of the squares:
590.1-590.45 = -0.35; (-0.35)² = 0.1225
590.2-590.45 = -0.25; (-0.25)² = 0.0625
590.3-590.45 = -0.15; (-0.15)² = 0.0225
590.4-590.45 = -0.05; (-0.05)² = 0.0025
590.5-590.45 = 0.05; (0.05)² = 0.0025
590.6-590.45 = 0.15; (0.15)² = 0.0225
590.7-590.45 = 0.25; (0.25)² = 0.0625
590.8-590.45 = 0.35; (0.35)² = 0.1225
(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8
= 0.42/8 = 0.0525 ≈ 0.053
(a) The mean of the glass parts rounded to nearest tenths of millimeters
= 590.45 and (b) Variance in tenths of millimeters is = 0.053 mm.
What is mode ?In a given set of data one which repeats most frequently is called the mode of the given data set.
To obtain the mean we add together all of the values and divide by the number of data values.
590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6
There are 8 data values; this gives us
4723.6/8 = 590.45
To find the variance, we subtract each of the data values from the mean and we square this difference to find the mean of the squares.
590.1-590.45 = -0.35; (-0.35)² = 0.1225
590.2-590.45 = -0.25; (-0.25)² = 0.0625
590.3-590.45 = -0.15; (-0.15)² = 0.0225
590.4-590.45 = -0.05; (-0.05)² = 0.0025
590.5-590.45 = 0.05; (0.05)² = 0.0025
590.6-590.45 = 0.15; (0.15)² = 0.0225
590.7-590.45 = 0.25; (0.25)² = 0.0625
590.8-590.45 = 0.35; (0.35)² = 0.1225
(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8
= 0.42/8 = 0.0525 and rounded to tenths of millimeters is 0.053
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two sides of a right triangle Measure 11 in and 15 in.
Part A
Use decimals rounded to the nearest tenth to complete the following statement. The length of the third side of the triangle could be ________ inches or ________ inches.
Part B
Write two side of the equations that justify your answers to Part A.
The sides could be 10.2 inches or 15.7 inches.
See the attached picture for the equations:
An arc is intercepted by a central angle of 3π2 radians on a circle with a radius of 18 centimeters. What is the exact length of the arc? Enter your answer, in terms of π , in the box.
Answer:
The length of the arc is [tex]27\pi \ cm[/tex]
Step-by-step explanation:
step 1
Find the circumference
we know that
The length of a complete circle is equal to the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=18\ cm[/tex]
substitute
[tex]C=2\pi (18)[/tex]
[tex]C=36\pi\ cm[/tex]
step 2
we know that
A central angle of [tex]2\pi[/tex] radians subtends the circumference of [tex]36\pi\ cm[/tex]
so
by proportion
Find the length of the arc by a central angle of [tex]\frac{3\pi }{2}[/tex] radians
[tex]\frac{36\pi }{2\pi}\frac{cm}{radians}=\frac{x}{(3\pi/2)}\frac{cm}{radians} \\ \\x=18*(3\pi/2)\\ \\x=27\pi \ cm[/tex]
The height, f(x), of a bouncing ball after x bounces is represented by f(x) = 80(0.5)^x. How many times higher is the first bounce than the fourth bounce?
A.
2
B.
4
C.
6
D.
8
Answer:
D) 8
Step-by-step explanation:
Given function for height = f(x) = 80(0.5)^x
It shows that the height of ball after any bounce can be calculated by putting bounce number in place of x in this equation.
so, height after first bounce f(1) is calculated by placing 1 in place of x
f(1) = 80(0.5)^1
f(1) = 80(0.5)
f(1) = 40
Similarly, the height after 4th bounce f(4)
f(4) = 80(0.5)^4
f(4) = 80(0.0625)
f(4) = 5
Therefore, the height of 1st bounce is 40/5 = 8 times higher than the fourth bounce. So, option D is correct.
The first bounce is 8 times higher than the fourth bounce. Option D (8) is correct.
The height of the bouncing ball is given by the function f(x) = 80(0.5)^x, where x represents the number of bounces. To find how many times higher the first bounce is than the fourth bounce, we'll calculate the heights for f(1) and f(4) and then compare them.
Calculate the height after the first bounce (x = 1):Therefore, the first bounce is 8 times higher than the fourth bounce, corresponding to option D (8).
What percentage of the data values falls between the values of 3 and 24 in the data set shown?
What percentage of the data values falls between the values of 3 and 24 in the data set shown?
25%
50%
75%
100%
25%
50%
75%
100%
Answer: 100%
Step-by-step explanation:
We are given a Box- plot, in which the minimum value is described by the left whisker is 3 and the maximum value is described by the right whisker is 24.
Since the range of all data values in a data is given from minimum value to the maximum value.
⇒ The percentage of the data values falls between the values of 3 and 24 in the data set shown = 100%
Tutor O-Rama claims that their services will raise student SAT math scores at least 50 points. The average score on the math portion of the SAT is μ=350 and σ=35. The 100 students who completed the tutoring program had an average score of 385 points. Is the students’ average score of 385 points significant at the 5% and 1% levels to support Tutor O-Rama’s claim of at least a 50-point increase in the SAT score? (2 pts) Is the Tutor O-Rama students’ average score of 385 points significantly different at the 5% and 1% levels from the average score of 350 points on the math portion of the SAT? What conclusion can you make, based on your results, about the effectiveness of Tutor O-Rama’s tutoring? (2 pts)
Answer:
See below
Step-by-step explanation:
The score increase was 35 points. They claimed an increase of at least 50 points. For a significance level of 5%, the z-score for the situation needs to be at smaller than -1.645. For a significance level of 1%, the z-score needs to be smaller than -2.325
The z score for our situation: z = (385 - 350)/50 = 0.7
The average score of 385 of Tutor O-Rama scores is not significantly different from the average of the other students SAT scores. The evidence doesn't support their claim of being effective tutoring.