Answer:29
Step-by-step explanation:
In Mr. Patterson’s class, the average score among students who studied for an exam was 78. The average among students who did not study was 54. The overall class average was 70. What portion of the class did not study? Express your answer as a common fraction.
this is the question
Using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ a=\sqrt[]{c^2-b^2} \\ a=\sqrt[]{25^2-17^2} \\ a=\sqrt[]{336} \\ a=4\sqrt[]{21}\approx18.3 \end{gathered}[/tex]the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. if a bank has an interest rate at the 45th percentile, what is the interest rate at this bank?
The interest rate at the bank = 2.324 %
Let X be the random variable representing the interest rate on a five-year certificate of deposit (cd) for banks in South Florida in 2018.
Then X follows the Normal Distribution with,
Mean, μ = 2.28 % and,
Standard Deviation, σ = 0.37 %
We need to find the X at the 45th percentile.
45th percentile implies z-value = 0.45
The z-score at 45th percentile or 0.45 probability = -0.12 [From the z-tables]
We have, z = (x-μ)/σ
⇒ zσ = x-μ
⇒ x = zσ+μ
⇒ x = (0.12 x 0.37) + 2.28
= 2.324
Hence the interest rate at the bank = 2.324 %
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Use matrices to write the equation of the function in the form y = Ax? + Br + C that contains the points (0, 1), (-2, 15), (3,10).
The most appropriate choice for matrices will be given by-
Required Equation
[tex]y = 2x^2 - 3x + 1[/tex]
What are matrices?
If the numbers are arranged in the form of rows and columns, then the arrangement is called matrix.
Here,
The equation is [tex]y =Ax^2 + Bx + C[/tex]
The function contains the points (0, 1), (-2, 15), (3,10).
On putting these coordinates in the equation,
C = 1
[tex]15 = A(-2)^2 + B(-2) + 1\\4A - 2B = 15-1\\2(2A - B ) =14\\2A - B = \frac{14}{2}\\2A -B = 7[/tex]................ (1)
[tex]10 = A(3)^2 + B(3) + 1\\9A + 3B = 10-1\\3(3A + B ) =9\\3A + B =\frac{9}{3}\\3A + B = 3[/tex].................... (2)
Here matrix method will be used
Let
[tex]P = \begin{bmatrix} 2 & -1\\ 3 & 1 \end{bmatrix}[/tex], [tex]Q = \begin{bmatrix} x \\ y\end{bmatrix}[/tex], [tex]R = \begin{bmatrix} 7\\3 \end{bmatrix}[/tex]
PQ = R
[tex]Q = P^{-1}R[/tex]
Adjoint P =
[tex]\begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}^T\\\\\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}[/tex]
Det P = [tex]\begin{vmatrix} 2 & -1\\3&1\end{vmatrix}[/tex]
= [tex]2\times 1 - 3 \times (-1)\\5[/tex]
[tex]P^{-1} = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}[/tex]
[tex]Q = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\begin{bmatrix}7\\3\end{bmatrix}[/tex]
[tex]Q = \frac{1}{5}\begin{bmatrix} 10\\-15\end{bmatrix}\\Q= \begin{bmatrix} 2\\-3\end{bmatrix}[/tex]
A = 2, B = -3
Required Equation
[tex]y = 2x^2 - 3x + 1[/tex]
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Complete Question
Use matrices to write the equation of the function in the form [tex]y = Ax^2 + Bx + C[/tex]that contains the points (0, 1), (-2, 15), (3,10).
Estimate what fraction of the 900-mile trip the car has traveled. Write your answer in simplest form.
Based on the distance of the entire trip, the fraction of the trip that the car has travelled is 514 ²/ ₇.
How far has the car gone?The diagram is divided into 7 parts which means that each part can be said to be:
= 1/7 of the journey
The car is in the 4th part so that means that the fraction of the trip that has been traveled is:
= 4 / 7
Given the total miles of the trip, this would be:
= 4/7 x 900
= 514.29
= 514 + 29 / 100
= 514 ²/ ₇
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20) g(a) = a² - 2
h(a) = -3a
Find g(a) + h(a)
The value of g(a) + h(a) is a²-3a-2 or (a-2)(a-1) using addition of functions.
What is the Function?Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where x belongs to X and y belongs to Y, with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y
Adding two functions-
g(a) = a²- 2
h(a) = -3a
Let h(a) be g(a) + h(a)
So h(a) = a² - 2 - 3a.
We can factorize the function into (a-2)(a-1).
So we get h(a) = (a-2)(a-1).
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what is the anwser
-2|7x-1|= 14
Answer: -3/4
Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.
Nice helping out!
Answer:
There are no solutions.
Step-by-step explanation:
Hello!
Isolate the absolute value equation first:
-2|7x - 1| = 14|7x - 1| = -7Now stop and think.
An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.
So the solution is No Solutions.
ASAP PLEASEEE HELPPP PLEASEEEE
1.If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, what transformation occurs from f(x) to h(x)?
A.Shift left 3 units
B.Shift right 3 units
C.Shift up 3 units
D.Shift down 3 units
2. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the vertex affected? Select all that apply.
A.The vertex will not change.
B.The vertex will shift right 3 units.
C.The vertex will shift left 3 units.
D.The vertex will shift up 3 units.
E.The vertex will shift down 3 units.
F.The vertex will not move up or down.
G.The vertex will not move right or left.
3. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the range affected?
A.The range will not change.
B.The range will be all real numbers.
C.The range will change from y ≥ 0 to y ≥ -3.
D.The range will change from x ≥ 0 to x ≥ -3.
1) A translation of 3 units down, option D.
2) The vertex moves 3 units down.
3) The new range is y ≥ -3, correct option is C.
Which transformation is applied?For a function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N
In this case, we have:
f(x) = |x|
h(x) = |x| - 3
Then h(x) = f(x) - 3
This is a shift of 3 units down, the correct option is D.
How is the vertex affected?
The vertex is translated 3 units down, like the whole graph of the function.
How is the range affected?
The vertex defines the minimum of the range, so if the vertex goes 3 units down, then the range also does, the new range will be:
y ≥ -3.
So the correct option is C.
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1/2 n + 3/4 n = 1/2
Solve for n =
Answer:
n=2/5
Step-by-step explanation:
Please look at the image below! :D
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex] [tex]\frac{1}{2}[/tex] means the same as [tex]\frac{2}{4}[/tex]
[tex]\frac{2}{4}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex]
[tex]\frac{5}{4}[/tex] n = [tex]\frac{1}{2}[/tex] multiply each side by [tex]\frac{4}{5}[/tex]
[tex](\frac{4}{5})[/tex][tex]\frac{5}{4}[/tex] n = [tex](\frac{4}{5})[/tex][tex]\frac{1}{2}[/tex]
n = [tex]\frac{4}{10}[/tex] = [tex]\frac{2}{5}[/tex]
For the following equation, complete the given ordered pairs, and use the results to graph the solution set for the equation.
Given:
[tex]y=-\frac{3}{4}x+1[/tex]Aim:
We need to graph the given function.
Explanation:
Replace x =-4 in the given equation.
[tex]y=-\frac{3}{4}(-4)+1[/tex][tex]y=-3(-1)+1[/tex][tex]y=3+1[/tex][tex]y=4[/tex]We get the point (-4, 4).
Replace x = 0 in the given equation.
[tex]y=-\frac{3}{4}(0)+1[/tex][tex]y=1[/tex]We get the point (0,1).
Replace x =4 in the equation.
[tex]y=-\frac{3}{4}(4)+1[/tex][tex]y=-3+1[/tex][tex]y=-2[/tex]We get the point ( 4, -2).
Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.
Final answer:
[tex](-4,4),\text{ }(0,1),\text{ }(4,\text{ -2}).[/tex]The graph of the given eqaution:
2/3x - 8 when x = 12
1) For this question, all we need to do is to plug it in the value for x.
So,
2/3x -8 =0 Plugging into x the value x=12
2/3(12) -8 =0
8 -8 =0
0
So when x=12, then the equation is equal to zero. This leads us to conclude that 12 is the root or the solution of this equation.
Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is 450450450 kilograms (\text{kg}kgstart text, k, g, end text), but Renna and her load of identical packages mass a total of 620\,\text{kg}620kg620, start text, k, g, end text. Each package has a mass of 37.4\,\text{kg}37.4kg37, point, 4, start text, k, g, end text.
Write an inequality to determine the number of packages, ppp, Renna could remove from the elevator to meet the mass requirement.
pls help
The inequality to determine the number of packages Renna could remove from the elevator to meet the mass requirement is 620 - 37.4g = 450.
What is an inequality?An inequality is simply used to show the relationship between the expressions that are not equal.
The mass limit is given as 450 grams. Renna has a package that has a weight of 620g.
Each package has 37.4g.
Let the number of packages to remove be p.
The expression will be:
= 620 - (37.4 × p) = 450
620 - 37.4g = 450.
This illustrates the concept of inequality.
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Alfred and Rani both picked different two-digit numbers. If you multiply Alfred's number by 5 and double Rani's number, the sum is 300. If you double
Alfred's number and multiply Rani's number by 3, the sum of the two numbers is 252. What is the sum of their two numbers?
O 96
O 112
O 128
O 144
O 150
Sr-85 used on bone scans it has a half life of 64.9 days fine the remaining amount after 100 days
The remaining amount of the substance with the half life of 64.9 days after 100 days is 2.749.
How can the remaining amount of the substance be calculted?To calculate the amount that remains after 100 days, this formular can be used
amount remaining = [tex]a (0.50)^{\frac{t}{h} }[/tex]
where t is the time that was required for the process to take place, where t is 100 days.
h is the halftime, which is been given as 64.9 days
where a is given as the initial amount that is present which is 8.
Then the values can be substituted to have
[tex]=a (0.50)^{\frac{100}{64.9} }[/tex]
= 2.749
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Write an equation of a line that is parallel to the
given line. Then, write one that is perpendicular.
x = -4
Answer:
X=ℝ, Y=ℝ
Step-by-step explanation:
Parallel means they have the same slope so it can be anything on the x-axis, perpendicular meaning opposite slope which is y=.
Simply the equation 3(6+x)=-18
Answer 3(6 + x) = -18 is 3
Explanation.-18 = 3(6 + x)
-18 = 18 + 3x
3x = 18 - 18
x = 0 + 3
x = 3
____________________
Class: High School
Lesson: Equation
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?
The truck can haul 1102 pounds.
According to the question,
We have the following information:
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.
(We will not directly convert ton into pounds. We will follow the following steps.)
Now, we know that 1 ton is equal to 1000 kilograms.
So, half ton makes 500 kg.
Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.
1 kg = 2.205 pounds
500 kg = (500*2.205) pounds
500 kg = 1102.5 pounds
Hence, the truck can haul 1102.5 pounds.
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₁ d 4. Ca are not to scale): 3,4 cm 37 mm 3,2 cm 4,3 cm b) 0.3. Calculate the perimeter of the polygons in centimeters
Shane is a building engineer and is determining the length of an access ramp needed to reach a step 1.5 feet off the ground. He knows the length of the ramp, r, in feet, can be expressed with the equation below.First, Shane finds that sin(4.5°) ≈ 0.08. Using his calculator, he then calculates the length of the ramp as shown below.What could Shane do to make his calculation more accurate? A. Use sin(4.5°) in his calculator instead of 0.08. B. Remeasure the angle with a different tool. C. Use the Pythagorean theorem to find the length of the ramp. D. Use a different trigonometric function to find the length of the ramp.
Statement Problem: Shane is a building engineer and is determining the length of an access ramp needed to reach a step 1.5 feet off the ground. He knows the length of the ramp, r, in feet, can be expressed with the equation below.
First, Shane finds that sin(4.5°) ≈ 0.08. Using his calculator, he then calculates the length of the ramp as shown below.
What could Shane do to make his calculation more accurate?
Solution:
The length of the ramp, r, in feet is expressed using the sine ratio;
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \sin 4.5^o=\frac{1.5}{r} \\ r=(\frac{1.5}{\sin 4.5})ft \\ \end{gathered}[/tex]Hence, Shane's calculation would be more accurate if he uses sin (4.5 degrees) in his calculator instead of 0.08
CORRECT OPTION: A
Two studies were done on the same set of data, where study a was a two-sided test and study b was a one-sided test. The p-value of the test corresponding to study a was found to be 0. 40. What is the p-value for study b?.
The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.
Therefore, the p-value for study b exists 0.080.
What is meant by p-value?The P value is the likelihood, for a particular statistical model, that the statistical summary would be either equal to or more extreme than the actual observed results if the null hypothesis were to hold.
In a two tailed test the probability of occurrence exists the total area beneath the critical range of values on both the sides of the curve (negative side and positive side)
Therefore, the probability values for a two tailed test as compared to a one tailed test exists given by the under given relation -
[tex]$p-\text { value }=P\left(Z < -\frac{\alpha}{2}\right)+P\left(Z > \frac{\alpha}{2}\right)$$[/tex]
simplifying the above equation, we get
[tex]$P \frac{\alpha}{2}=0.040$[/tex]
Substituting the given value in above equation, we get -
Probability values for a two tailed test
= 0.040 + 0.040
= 0.080
Therefore, the p-value for study b exists 0.080.
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math pease help me i need it now asap
1. The mathematical expression for the length is C. 2x + 5.
2. The quadratic equation is A. 2x² + 5x - 18 = 0.
3. The width of the tarpaulin is A. 2 ft.
4. The length of the tarpaulin is D. 9 ft.
5. The perimeter of the tarpaulin is C. 22 feet.
How to calculate the value?From the information, the following can be deduced:
Width = x
Length = (2 × x) + 5 = 2x + 5
Area = 18 ft²
The equation will be:
Length × Width =Area
(2x + 5)x = 18
2x² + 5x = 18
2x² + 5x - 18 = 0
2x² - 4x + 9x - 18 = 0
2x(x - 2) + 9(x - 2)
Therefore, x - 2 = 0
x = 0 + 2 = 2
Width = 2
Length = 2x + 5 = 2(2) + 5 = 9ft
Perimeter = 2( Length + Width)
= 2(2 + 9)
= 22 feet.
This illustrates the concept of addition to calculate the perimeter.
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Formula to work out the surface area of half a cylinder
Formula to work out the Total surface area of half-cylinder = [tex]\pi rh + \pi r^{2} + 2rh[/tex]
To find:
Formula to work out the surface area of half a cylinder
Solution:
The surface area of a semi-cylinder can be calculated by adding half the curved area of the cylinder to the area of the two semi-circles and the area of the rectangular section below. The formula for the surface area of a semi-cylinder is given by: Total surface area of
Total surface area of a half-cylinder = (1/2) × curved area of cylinder + 2 × area of semi-circle + area of base of cylinder.
total surface area of a half-cylinder = [tex]\pi rh+\pi r^{2} +2rh[/tex]
where r = radius of cylinder
[tex]\pi[/tex] = 3.14 or 22.7 cm
h = height of cylinder
(Or) We can find Total surface area of half cylinder as, Total surface area of half cylinder ÷ 2
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In Emily's physics class, she had to solve the equation 9 = 12at2 + ut for u. Each step of her work is shown below.
Use the drop-down menus to explain each step.
The equation of u when it is the subject is u = 9/t - 12at
How to determine the solution for the equation for u?From the question, the original equation is given as
9 = 12at2 + ut
Next, we rewrite the equation to show the exponents
This is represented as
9 = 12at² + ut
To solve further, we simply isolate the variable term ut
This is done by subtracting 12at² from both sides of the equation
So, we have the following equation
9 - 12at² = 12at² - 12at² ut
Evaluate the like terms in the equation
So, we have
9 - 12at² = ut
Lastly, divide both sides of the equation by t
So, we have
(9 - 12at²)/t = ut/t
Evaluate the quotients
9/t - 12at = u
Make us the subject
u = 9/t - 12at
Hence, the solution for the equation for u is u = 9/t - 12at
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2 What is the slope of the line in the picture below?
Explanation
if you know 2 points of a line you can easily find the slope using
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(-1,5)
P2(7,1)
replace,
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{1-5}{7-(-1)} \\ \text{slope}=\frac{-4}{7+1}=-\frac{4}{8}=-\frac{1}{2} \\ \text{slope}=-\frac{1}{2} \end{gathered}[/tex]I hope this helps you
You had $21 to spend on five notebooks after buying them u had $6 dollars how much did each notebook cost.
Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:
[tex]5x[/tex]We had 21 dollars and we spent 5x on the notebooks, this can be express as:
[tex]21-5x[/tex]Finally we know that this is equal to the six dollars we had at the end, then we have the equations:
[tex]21-5x=6[/tex]Solving for x we have:
[tex]\begin{gathered} 21-5x=6 \\ 21-6=5x \\ 5x=15 \\ x=\frac{15}{5} \\ x=3 \end{gathered}[/tex]Therefore each notebook cost $3
A rectangles width (W) is 5 inches more than a third the length (L). If the perimeter is 42 inches what are the dimensions of the rectangle ?
The length and width of the rectangle are 5.5 inches and 10.5 inches.
What do we mean by rectangles?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry.It can also be explained in terms of a parallelogram with a right angle or an equiangular quadrilateral—a quadrilateral whose angles are all equal.A square is an asymmetrical shape with four sides of equal length.So, the dimensions of the rectangle:
Let the length of the rectangle be 'x' and the width be 'x + 5'.The perimeter is 42 inches.Perimeter formula: 2(l + b)Substitute the values in the formula as follows:
P = 2(l + b)42 = 2(x + x + 5)42 = 2(2x + 5)42 = 4x + 204x = 42 - 204x = 22x = 22/4x = 5.5 inches (Length)x + 5 = 5.5 + 5 = 10.5 inches (Width )Therefore, the length and width of the rectangle are 5.5 inches and 10.5 inches.
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a finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term. for example, such a sequence might begin with the terms 247, 475, and 756 and end with the term 824. let be the sum of all the terms in the sequence. what is the largest prime factor that always divides ?
The largest prime factor that always divides the sum of the terms in the sequence is 37.
The sequence is finite and consists of three-digit integers.
The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.
From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.
Let "x" be the sum of the digits at unit place in all the terms.
The sum of all the terms is "S".
S = 111*x
S = 3*37*x
We can clearly see that the sum "S" is divisible by 37.
Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.
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Which ordered pair would form a proportional relationship with the point graphed below?
Answer:
(5, 20)
Step-by-step explanation:
(5, 20) is the only ordered pair which falls on the line
order the fractions 4/5, 1/2,9/10,3/4 from least to greatest
Answer:
1/2 -> 3/4 -> 4/5 -> 9/10
Step-by-step explanation:
1/2 = 50%
3/4 = 75%
4/5 = 80%
9/10 = 90%
How to figure out:
1/2 - Divide 100/2 = 50. So 1/2 of 100 is 50 so 50%
3/4 - Divide 100/4 = 25. Now multiply 25 x 3 = 75 so 75%
4/5 - Divide 100/5 = 20. Now multiply 20 x 4 = 80 so 80%
9/10 - Divide 100/10 = 10. Now multiply 10 x 9 = 90 so 90%
If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours.
A table showing Rate in part per hour, Time in hours, and Part of Project Completed. The first row shows Judy, and has, question mark, 2, and StartFraction 2 Over 3 EndFraction. The second row shows Sal, and has, r, r, and 2 r.
What is the missing value from the table that represents Judy's rate?
r
3 – r
StartFraction 1 Over 3 EndFraction.
3
The missing value is 1/3 from the table that represents Judy's rate which is the correct answer that would be an option (C).
What is the relation?In mathematics, relations are used to describe the link between the components of two sets. They aid in mapping items from one set (known as the domain) to elements from another set (known as the range), resulting in ordered pairs of the form (input, output).
We have been given the rates of time taken by Judy and Sal to complete a puzzle.
Sal's rate is r, as we can see from the table. Judy is said to take 3 hours to solve a puzzle by herself. It barely takes them two hours to work with Sal.
Because Judy completes the task in three hours, the portion of the puzzle finished in one hour is 1/3.
Therefore, the missing value is 1/3 from the table that represents Judy's rate
Hence, the correct answer would be an option (C).
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