Answer:
a) Positive linear
b) 72
c) Marks scored when no time is spend on homework.
Step-by-step explanation:
a) relationship between the hours spent on homework and the test scores
As the time spent on homework increases the test score increases.
Similarly if less time is spent on homework, there would be a decrease in test score.
The two variables are directly related.
Thus, there relationship can be expressed as a positive linear relationship.
b) The model function
[tex]y= 8x + 40[/tex]
where y is the test score and x is the time spent on homework in hours.
Score predicted by model when x = 4
[tex]y(4)= 8(4) + 40 = 32 +40 = 72[/tex]
Thus, model predict that the score on test will be 72 when 4 hours are spent on homework.
c) Interpretation of 40
When x = 0
[tex]y(0)= 8(0) + 40 = 40[/tex]
Interpretation:
Thus, when Paul spends no time on homework that is zero hours are spend on homework, then, Paul will score 40 on test.
How many tens are in 50,000
(a) How far does a car travel if it moves at 52 miles per hour for 3.5 hours?
Answer:
182 miles
Step-by-step explanation:
52 times 3.5=182
The Answer is 182 miles
When multiplying 52 by 3.5 you'll get 182 as the product
Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a 1, 2, or 3, Gabriel gives Alyssa $4. If Alyssa rolls a 4 or 5, Gabriel gives Alyssa $1. However, if Alyssa rolls a 6, she gives Gabriel $12.
a) Determine Alyssa's expectation.
b) Determine Gabriel's expectation.
11.3 #12
Answer:
Part a) Alyssa's expectation is equal to $0.33
Part b) Gabriel's expectation is equal to -$0.33
Step-by-step explanation:
we know that
The expected value is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss).
Part a) Determine Alyssa's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
The probability is 3/6
so
we have
[tex]\frac{3}{6}(4)=\$2[/tex]
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
The probability is 2/6
so
we have
[tex]\frac{2}{6}(1)=\$0.33[/tex]
3) if Alyssa rolls a 6, she gives Gabriel $12
The probability is 1/6
so
we have
[tex]-\frac{1}{6}(12)=-\$2[/tex] ---> is negative because is a loss
therefore
Alyssa's expectation is equal to
[tex]\$2+\$0.33-\$2=\$0.33[/tex]
Part b) Determine Gabriel's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
Is a loss for Gabriel
The probability is 3/6
so
we have
[tex]-\frac{3}{6}(4)=-\$2[/tex] ---> is negative because is a loss
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
Is a loss for Gabriel
The probability is 2/6
so
we have
[tex]-\frac{2}{6}(1)=-\$0.33[/tex] ---> is negative because is a loss
3) if Alyssa rolls a 6, she gives Gabriel $12
Is a win for Gabriel
The probability is 1/6
so
we have
[tex]\frac{1}{6}(12)=\$2[/tex]
therefore
Gabriel's expectation is equal to
[tex]-\$2-\$0.33+\$2=-\$0.33[/tex]
The expected outcomes for both Alyssa and Gabriel from the game are $0. This is calculated using the probabilities of each outcome and their respective gains or losses.
Explanation:In the game between Alyssa and Gabriel, we are to calculate the expected outcomes for both players. To calculate the expectation, we will weigh the possible outcomes ($4, $1, -$12 for Alyssa and -$4, -$1, $12 for Gabriel) by their probabilities.
The dice has six faces, so the probability for each outcome is determined by the number of corresponding faces divided by six. Let's calculate the expectation for both:
Alyssa's expectation: (1/2 * $4) + (1/3 * $1) - (1/6 * $12) = $2 - $2 = $0. Gabriel's expectation: -(1/2 * $4) - (1/3 * $1) + (1/6 * $12) = -$2 + $2 = $0.
So, both Alyssa and Gabriel have an expected gain of $0 from this game.
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Name the property shown by each statement and which is associative or commutation or simply
Answer:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.
The Commutative property states that order does not matter. Multiplication and addition are commutative.
hope this helps please mark brainliest!
9 yd
12 yd
What is the length of the hypotenuse?
Answer:
Hi there!
The correct answer will be 15 yd
Step-by-step explanation:
There are two ways you can go about solving this problem
Method One: Pythagorean Theorem
a^2 + b^2 = c^2 then all you have to do is plug in the values
(12)^2 + (9)^2 = c^2 you should get c^2 = 225 then you square root both sides and you get c = 15
Method Two: Pythagorean Identities
This triangle represents a 3,4,5 triangle
All the sides just tripled so that means the hypotenuse is 5*3 which equals 15
Is 4/6 is farther from 1/2
Answer: Yes
sdizjaoijf
Use the quadratic formula to solve the equation
Answer:
=3
=2
Step-by-step explanation:
12−5+6=0
using the Quadratic Formula where
a = 1, b = -5, and c = 6
=−±2−4‾‾‾‾‾‾‾‾√2
=−(−5)±(−5)2−4(1)(6)‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(1)
=5±25−24‾‾‾‾‾‾‾√2
=5±1‾√2
The discriminant 2−4>0
so, there are two real roots.
Simplify the Radical:
=5±12
=62=42
which becomes
=3
=2
hope this helps :)
Ariyonne claims that (6,3) is the point of intersection of the lines y=4x-2 and y=1/2x+5. Is she correct? How do you know ?
In order to solve the following system of equations by subtraction, which of
the following could you do before subtracting the equations so that one
variable will be eliminated when you subtract them?
4x – 2y = 7
3x – 3y=15
A. Multiply the top equation by 1/3
B. Multiply the top equation by 3 and the bottom equation by 4.
C. Multiply the top equation by-3 and the bottom equation by 2.
D. Multiply the top equation by 15 and the bottom equation by 7.
Answer:
B
Step-by-step explanation:
B produces the term 12x that cancels out after subtraction.
In order to eliminate one variable by subtracting, you should multiply the top equation by -3 and the bottom equation by 2. In doing so, this will make the coefficients of y equal and opposite, allowing this variable to be eliminated when the two equations are added together.
Explanation:The question relates to the method of solving a system of linear equations by subtraction. In order to eliminate one variable when subtracting these equations, we would need to manipulate the equations such that the coefficients of one variable are exact opposites. Hence, the objective is to make the coefficients of y, -2 and -3, opposite each other.
To achieve this, the correct answer is C. Multiply the top equation by -3 and the bottom equation by 2.
By performing these multiplications we'll have:
-12x + 6y = -21.
6x - 6y = 30.
Now, if we add these two equations, we'll be able to eliminate the y variable and can proceed to solve for x.
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The sum of two numbers is 141. One number is 37 more than the other. Find the numbers
Answer:
104
Step-by-step explanation:
x+37=141
subtract 37 from both sides
-37=141-37
x= 104
Step-by-step explanation:
x = First number
x + x + 37 = 141 (Because we know that the 2nd number is 37 more than the first, we can just say x + 37.)
2x + 37 = 141 (Combine like terms.)
2x = 104 (Subtract 37 from both sides.)
x = 52 (Divide 2 from both sides.)
Now we know that the first number is 52. Now we just add the 37 to 52 to find the second number.
37 + 52 = 89 = Second number
Proof: 52 + 89 = 141
Fill in the blank to make a true equation. (-9)(___) = 36 A. - 4 B. 4 C. 6 D. - 6
Answer:
Option A, -4
Step-by-step explanation:
Step 1: Make an equation to represent the problem
(-9)(x) = 36
Step 2: Solve for x by dividing both sides by -9
-9x / -9 = 36 / -9
x = -4
Answer: Option A, -4
An art supply store typically sells bottles of green paint for every 9 bottles of aqua paint. How many bottles of aqua paint does it sell when it sells 30 bottles of green paint?
Final answer:
The store sells 270 bottles of aqua paint when it sells 30 bottles of green paint.
Explanation:
To find out how many bottles of aqua paint the store sells when it sells 30 bottles of green paint, we can set up a proportion. Since the store sells 9 bottles of aqua paint for every 1 bottle of green paint, we have the ratio 9/1. We can set this equal to the unknown quantity, x, over 30 (the number of green paint bottles).
9/1 = x/30
Next, cross multiply to solve for x. Cross multiplying gives us:
9 * 30 = 1 * x
Simplifying this equation gives us:
270 = x
Therefore, the store sells 270 bottles of aqua paint when it sells 30 bottles of green paint.
what is 2 and 1 4th times 1 and 1 half
Answer:
3 3/8
Step-by-step explanation:
4-2y+3=-9
What is y?
y = 8
hope this helps :)
Find, to the nearest degree, the angle of elevation of the sun when a person 170 cm tall casts of shadow 220 cm long.
Trigonometry
Answer:
Θ = 52°
Step-by-step explanation:
Once you've set up the triangle, you can see that the adjacent side is 170 cm and the opposite side is 220 cm.
tanΘ = [tex]\frac{220}{170}[/tex]
Θ = tan-1 (220/170)
Θ = 52°
The angle of elevation of the sun when a person 170 cm tall casts of shadow 220 cm long is 37.694°.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
A person 170 cm tall casts of shadow 220 cm long.
Then the angle will be
[tex]\rm tan \theta = \dfrac{Perpendicular }{Base}[/tex]
We have
Perpendicular = 170 cm
Base = 220 cm
Then
[tex]\rm tan \theta = \dfrac{170}{220}\\\\\\ \theta \ \ \ \ = tan^{-1} \dfrac{170}{220}\\\\\\\theta \ \ \ \ = 37.694^o[/tex]
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The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers.
The small number is 2.
The large number is 3.
Step-by-step explanation:
Let the two consecutive numbers be x and x+1.
x be the small integer.x+1 be the large integer.The sum of these two consecutive integers = small integer + large integer
The sum of these two consecutive integers is x+x+1 = (2x+1)
It is given that,
The sum of two consecutive integers is one less than three times the smaller integer.This means that, (2x+1) is one less than three times the smaller integer.Here, the small integer is represented as x.Therefore, it can determined that :
(2x+1) = 3x-1
Keeping x term on one side and constants on other side,
3x-2x = 1+1
x = 2
Therefore, the small number is 2 and the large number is x+1 = 3.
The wholesale price for a pair of shoes is $8.50. A certain department store marks up the wholesale price by 90%. Find the price of the pair of shoes in the department store. Round your answer to the nearest cent, as necessary.
Answer:
$16.15
Step-by-step explanation:
The wholesale price:
$8.50Selling Price:
$8.50 + 90% = $8.50 *1.9 = $16.15Pair of shoes sold for $16.15 in the store
The department store marks up the wholesale price by 90%, equating to $7.65. Adding this to the original wholesale price of $8.50, the retail price of the shoes in the department store is $16.15.
Explanation:To calculate the retail price of the shoes in the department store, we need to add the markup value to the original wholesale price. The markup is 90% of the wholesale price. Therefore, we calculate 90% of $8.50, and then add that to the original price.
To find 90% of $8.50, we multiply $8.50 by 90/100. This gives us $7.65. This is the markup value.
We then add this markup value to the original wholesale price. So, $8.50 + $7.65 = $16.15.
The price of the pair of shoes in the department store is therefore $16.15.
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pLeAsE hElP! HuRrY!
Solve for A:
14a < 112
A.) a < -8
B.) a > 8
C.) a > -8
D.) a < 8
If one factor of x2 + 2x - 24 is (x+6), what is the other factor?
(x+8)
(x-8)
(x+4)
(x-4)
Answer:
( x - 4)
Step-by-step explanation:
x² + 2x - 24
From here, you must find the two factors of -24 (the first and third terms' coefficients multiplied together) that add up to 2 (the middle terms coefficient)
( x - 4) ( x + 6)
Other factor of x² + 2x - 24 is (x - 4).
What is factor?Factors and multiples are two related concepts in math. A factor is a number that divides the given number exactly with 0 as the remainder.
Given expression
x² + 2x - 24 has factor (x + 6)
So, the expression should be divisible by (x + 6)
(x² + 2x - 24)/(x + 6)
It can be written as
(x² + 6x - 4x -24)/(x + 6)
Factoring out common factor
(x (x + 6) - 4 (x + 6))/(x + 6)
factoring out common factor
(x + 6)(x - 4)/(x + 6)
Simplifying
= (x - 4).
Hence, (x - 4) is other factor of x² + 2x - 24.
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−4 5/9+8/9+ 0+0+0+0+0+0+0+0=
Answer:
-3.66666666668
Step-by-step explanation:
The zero's you do not have to add because they have to content or value.
-4 5/9 into improper = 31/9 = -4.55555555556
8/9 = 0.88888888888
ADD
[tex]\left\begin{array}{ccc}-4.55555555556\\+\\0.88888888888\end{array}\right\\---------[/tex]
-3.66666666668
Hope this helps you!
Have a good night! :)
Answer:
-3.66666666668
Step-by-step explanation:
Write an equivalent expression for x + x + x + 2x + x
Answer:
6x
Step-by-step explanation:
x + x + x + 2x + x
Simplify the equation
4x + 2x
6x
Hope this was useful to you!
U. AD-3
3. One of the acute angles in a right triangle has a measure of 34.6°. What is the measure of the other acute
angle?
a. 145.40
c. 55.4°
b. 34.6°
d. 90°
Solution:
Given that,
One of the acute angles in a right triangle has a measure of 34.6°
The sum of the three angles of a triangle is always 180 degrees.
Also, that the measure of a right angle is always 90 degrees
Let "x" be the other acute angle
Therefore,
x + 90 + 34.6 = 180
x + 124.6 = 180
x = 180 - 124.6
x = 55.4
Thus the measure of other acute angle is 55.4 degrees
Answer:
Yes, what the other person said
Step-by-step explanation: basically you subtract 90.0 - 34.6
table A
x y
4 1
8 2
12 3
16 4
Compare the table of Object A and the equation y = 5x of Object B. Which of the two moving objects has greater speed and by what factor? (round to nearest hundredth)
A) Object A by a factor of 1.05
B) Object B by a factor of 1.05
C) Object A by a factor of 1.25
D) Object B by a factor of 1.25
Answer:
D
Step-by-step explanation:
1. Find the rate of change of the graph. Which is 4.
2. Because 5 is greater of 4, Object B has the greater speed.
3. To find the factor you must divide 4 from 5. 5 ÷ 4
4. 5 ÷ 4 = 1.25
5. The correct answer is D
Answer:C)Object A by a factor of 1.25
Step-by-step explanation:this is the answer for USA test prep.
Helppppppppppppppppppp
The distance between two cities on a map is 4 1/2 inches. The actual distance between the two cities is 24 miles.
What is the scale used on the map?
If the scale on a different map of the same area is 1/4 inch = 1 mile, how many inches separate the same two cities?
Answer:
1 inch : 5⅓ miles
6 inches
Step-by-step explanation:
Map : Actual
4½ : 24
1 : 24/4.5
24 ÷ 9/2 = 24 × 2/9 =
1 inch on map represents an actual distance of 16/3 miles in actual
16/3 = 5⅓ miles
Map : Actual
¼ inch : 1 mile
X inch : 24
¼×24 = 6 inches
Answer: 3/16 inches : 1 mile
6 inches
Step-by-step explanation:
[tex]\dfrac{\text{Model}}{\text{Actual}}:\dfrac{4\frac{1}{2}\ inches}{24\ miles}\div\dfrac{24}{24}=\dfrac{\frac{3}{16}}{1}\quad \longrightarrow \quad \large\boxed{\dfrac{3}{16}\ inches:1\ mile}\\[/tex]
[tex]\dfrac{\text{Model}}{\text{Actual}}:\dfrac{\frac{1}{4}\ inches}{1\ mile}=\dfrac{x}{24\ miles}\\\\\\\text{Cross Multiply}:\quad \dfrac{1}{4}\bigg(24\bigg)=x\\\\.\qquad \qquad \qquad \qquad \quad \quad \large\boxed{6=x}[/tex]
the retail cost of a computer is 22% more than its wholesale cost. what is the whole sale cost?
Answer:5
Step-by-step explanation:
you do it
lily can travel 60 miles in 1.5 hours. If her speed is reduced by 5 mph,how har can she travel in 3 hours
Answer:
110
Step-by-step explanation:
Answer:
105 miles
Step-by-step explanation:
first we have to find her speed before it is reduced
so
60/1.5
thats equal to 40
she can travel 40 mph
reduce that by 5 so her speed is now 35mph
35*3=105
-4x + 26 = -2 whats x?
Answer:
The value of x is equal to 7
Step-by-step explanation:
if -4x + 26 = -2
-4x = -2 - 26
-4x = - 28
Divide both sides by -4, then we will have
x = -28/-4
x = 7
Steps to solve:
-4x + 26 = -2
~Subtract 26 to both sides
-4x + 26 - 26 = -2 - 26
~Simplify
-4x = -28
~Divide -4 to both sides
-4x/-4 = -28/-4
~Simplify
x = 7
Best of Luck!
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, -13, and 5 + 4i
f(x) = x4 - 8x3 - 12x2 + 400x - 1599
f(x) = x4 - 200x2 + 800x - 1599
f(x) = x4 - 98x2 + 800x - 1599
f(x) = x4 - 8x3 + 12x2 - 400x + 1599
Answer:
third option
Step-by-step explanation:
Given f(x) has zeros x = a, x = b, then
the factors are (x - a), (x - b) and the polynomial is the product of the factors.
Complex zeros occur as conjugate pairs, thus
5 + 4i is a zero then 5 - 4i is a zero
The zeros are x = 3, x = - 13, x = 5 + 4i, x = 5 - 4i, thus the factors are
(x - 3), (x - (- 13)), (x - (5 + 4i)), (x - (5 - 4i)), that is
(x - 3), (x + 13), (x - 5 - 4i), (x - 5 + 4i)
= (x - 3), (x + 13), ((x - 5) - 4i), ((x - 5) + 4i)
The polynomial is the product of the factors
f(x) = (x - 3)(x + 13)((x - 5) - 4i)((x - 5) + 4i) ← expand factors in pairs
= (x² + 10x - 39)((x - 5)² - 16i²) → i² = - 1
= (x² + 10x - 39)(x² - 10x + 25 + 16)
= (x² + 10x - 39)(x² - 10x + 41) ← distribute
= [tex]x^{4}[/tex] - 10x³ + 41x² + 10x³ - 100x² + 410x - 39x² + 390x - 1599 ← collect terms
= [tex]x^{4}[/tex] - 98x² + 800x - 1599
Answer:
The third option
Step-by-step explanation:
Consider the given statement. At least one gift in the bag is wrapped.
For each statement below, determine whether it is a negation of the given statement is True or False.
At least one gift in the bag is not wrapped.
Not every gift in the bag is wrapped.
Every gift in the bag is wrapped.
None of the gifts in the bag are wrapped.
Answer:
The negation to the given statement "At least one gift in the bag is wrapped - true" is " At least one gift in the bag is not wrapped" - False
At least one gift in the bag is not wrapped - False Not every gift in the bag is wrapped-True Every gift in the bag is wrapped-False None of the gifts in the bag are wrapped-FalseStep-by-step explanation:
Given statement is At least one gift in the bag is wrapped is true
The negation to the given statement is " At least one gift in the bag is not wrapped" - False
To determine whether the statement is a negation of the given statement is True or False :
At least one gift in the bag is not wrapped - False Not every gift in the bag is wrapped-True Every gift in the bag is wrapped-False None of the gifts in the bag are wrapped-False