For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
As given in the question,
For the saving account,
Amount deposited is directly proportional to the number of weeks
Let y be the amount deposited and x be the number of weeks
y ∝ x
y = kx
'k' is the constant of proportionality
As per data unit rate is measured in dollars per week
For y = $14 then x = 2 weeks
14 = 2k
⇒ k = $7
For y = $35 then x = 5weeks
35 =5k
⇒ k = $7
Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
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choose if the following statement is true or false: correlation is sensitive to the scale of the data; however, covariance is not sensitive to the scale of the data
Correlation is not sensitive to the scale of the data; however, covariance is sensitive to the scale of the data, so the statement is false.
Covariance is a term used in statistic and regression analysis. Covariance shows how two variables differ.
Covariance is affected by the change in scale, for example if all the value of one variable is multiplied by a constant and all the value of another variable are multiplied, by the same or another constant all together, then the covariance is automatically changed.
Correlation is also a term used in regression analysis and statistics. Correlation shows how two variables are related and therefore not influenced by the change in scale.
Hence the given statement is False
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9. Find the area of the shaded region.
22 cm
10 cm
7 cm
Find the value of x and XZ if Y is between X and Z, XY = 19, YZ = 2x+5,
and XZ = 6x + 12.
The values of x and XZ, calculated by the given equations are 3 and 30 respectively.
What is a equation?
The equals sign indicates that two expressions in an equation are equal. An equation is a mathematical formula. The meaning of the word equation and its cognates may change a bit depending on the language. An equation is defined as including one or more variables in French, as opposed to English, where an equation is defined as any well-formed formula that consists of two expressions connected by the equals sign.
Given information (and equations) in the question:
Y is between X and Z,
XY = 19,
YZ = 2x+5,
XZ = 6x+12
Since the question say Y is between X and Z, it means:
XY + YZ = XZ
Substituting the values in this equation by the values given in the question:
19 + 2x + 5 = 6x + 12
24 - 12 = 4x
x = 3
putting the value of x in the given equation:
XZ = 6x + 12
XZ = 6(3) + 12
XZ = 18 + 12
XZ = 30
Hence, the values of x and XZ are 3 and 30 respectively.
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Evaluate the expression when x=5The expression is 4x -13.
To answer this question, we only need to replace x by 5, and then solve the resulting operations:
[tex]x=5\Rightarrow4x-13=4\cdot(5)-13=20-13=7[/tex]Therefore, the value for the expression 4x-13 when x = 5 is equal to 7.
6.2: The Return of the Box
Earlier, we learned we can make a box from a piece of paper by cutting squares of side
length x from each corner and then folding up the sides. Let's say we now have a piece of
paper that is 8.5 inches by 14 inches. The volume V, in cubic inches, of the box is a
function of the side length x where V(x) = (14-2x)(8.5-2x)(x).
1. Identify the degree and leading term of the polynomial. Explain or show your
reasoning.
2. Without graphing, what can you say about the horizontal and vertical intercepts of
the graph of V? Do these points make sense in this situation?
The leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.
A sheet of paper measuring 8.5 inches by 14 inches is currently in our possession. The box's volume V, measured in cubic inches, depends on the side length x, where V (x) = (14-2x)(8.5-2x)(x).
So, we have :
V (x) = (14-2x)(8.5-2x)(x)
[tex]V(x) = (14-2x)(8.5-2x)(x).\\V (x) = (14-2x)(8.5x-2x^{2} )\\V(x) = 4x^{3} -45x^{2} + 119x[/tex]
Thus, the leading term of the polynomial is [tex]4x^{3}[/tex] and the degree of the polynomial is 3.
Now, we have :
[tex]V(x) = 4x^{3} -45x^{2} + 119x\\V(x) = x ( 4x^{2} -45x +119)\\V(x) = x (x-7)(4x-17)[/tex]
Now, For intercepts, V(x) = 0
[tex]V(x) = x (x-7)(4x-17) = 0\\x (x-7)(4x-17) = 0\\\\x = 0, 7, 4.25[/tex]
Now when x = 0, V(x) =0
when x = 7, f(x) = 135
when x = 4.25, f(x) = 252.89
So, the points are (7, 135) and ( 4.25, 252.89)
These points represent the value of x and their corresponding value of V.
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Please see attached question
The probability that the student is a sixth-grader or rated good grades as most important is (168 / 335) + (135 / 335) = 0.904
What is the probability?Probability is used to determine the odds that a random event would happen. The odds that the event would happen lies between 0 and 1.
The probability that the student is a sixth-grader or rated good grades as most important = (number of sixth-graders / total number of students) + (students who rates good grades as most important / total number of students)
(168 / 335) + (135 / 335) = 303 / 335 = 0.904
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∠1 and ∠2 are vetical angles. If m∠1 =(5x+12)° and m∠2 =(6x−11)°. m∠1=
⇒Vertical angles are equal .
This means that ∠1=∠2
⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.
[tex]5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23[/tex]
x=23°
To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:
[tex]< 1=5x+12\\=5(23)+12\\=127[/tex]
∠1=127°
What is the slope of the line that passes through the points (-4, -10)) and (-7, -19)
? Write your answer in simplest form.
Answer:
Slope = 3
Step-by-step explanation:
(-4, -10) and (-7, -19)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -19 - (-10) -19 + 10 -9
m = ------------ = ---------------- = ------------- = -------- = 3
x₂ - x₁ -7 - (-4) -7 + 4 -3
I hope this helps!
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{-7}-\underset{x_1}{(-4)}}} \implies \cfrac{-19 +10}{-7 +4} \implies \cfrac{ -9 }{ -3 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y +10= 3 (x +4) \\\\\\ y+10=3x+12\implies {\Large \begin{array}{llll} y=3x+2 \end{array}}[/tex]
What real-world knowledge did you use to understand the STEM Task?
The real world knowledge we use to understand the STEM task are :
A) STEM integrates it's concepts and applications to real life.
B) STEM helps in finding solution to the practical issues.
C) Focuses on building models and replicating scenarios.
What is STEM ?
STEM education refers to the integrated teaching and learning of the subjects such as science, technology, engineering, and mathematics.
We know that STEM teaches critical thinking skills and instills a passion for innovation. Beyond the advantages of learning STEM subjects, STEM supports the problem-solving and inquisitive learning that are essential for success in a range of tasks and professions. Colleges are now incorporating all of these helpful ideas into their normal study courses, and the results are clearly very favorable.
The real world knowledge we use to understand the STEM task is as follows :
STEM education stresses the application of knowledge to real-life situations while integrating concepts that are often taught as separate courses in various classrooms.Finding a solution to a practical issue is often the focus of a STEM lesson or unit, which frequently emphasizes project-based learning.Building models and replicating scenarios are common STEM instructional activities. Students' understanding of the relationship to the real world is ensured by a competent STEM lesson.Therefore , the real world knowledge we use to understand the STEM task are :
A) STEM integrates it's concepts and applications to real life.
B) STEM helps in finding solution to the practical issues.
C) Focuses on building models and replicating scenarios.
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Find 3 consecutive numbers whose sum is 132
Answer:
Integer 1- 43
Integer 2- 44
Integer 3- 45
Step-by-step explanation:
x+(x+1)+ (x+2)=132
3x+3-3=132-3
3x=127
/3 /3
x=43
x+1=44
x+2=45
If g :R → R is given by g(x) = x2 + 3 , find the function f such that (g. f) (x) = 4x2 + 3. A. 3x B. 4x C. 2x D. None of these
Given:
[tex]\begin{gathered} g(x)=x^2+3_{} \\ (g\circ f)(x)=4x^2+3 \end{gathered}[/tex][tex](g\circ f)(x)=g(f(x)[/tex]Let substitute one by one from the given options.
[tex]\begin{gathered} g(3x)=(3x)^2+3 \\ g(3x)=9x^2+3 \end{gathered}[/tex]3x is not the function f.
[tex]\begin{gathered} g(4x)=(4x)^2+3 \\ g(4x)=16x^2+3 \end{gathered}[/tex]4x is not the function f.
[tex]\begin{gathered} g(2x)=(2x)^2+3 \\ g(2x)=4x^2+3 \end{gathered}[/tex]2x is the function f.
[tex]f(x)=2x[/tex]Option C is the final answer.
Ahouseis13feettall.Itsshadowis40feetlongatthesametimetheshadowofanearbybuildingis340feetlong.Findtheheightofthebuilding.
the red triangle is the building
the black triangle is the house
x is the height of the building
we have a problem of Tales triangles semblants so we can use this equalities
[tex]\begin{gathered} \frac{x}{340}=\frac{13}{40} \\ x=\frac{13(340)}{40}=110.5\text{ f}eet \end{gathered}[/tex]the height of the building is 110.5 feet
Question 5 (05.05)Based on the graph, what is the initial value of the linear relationship?
4
1) Examining that graph, we can see that this is a decreasing function, due to the line direction. And that the initial value is the y-intercept.
2) Hence, the initial value is 4. Notice that all values after that goes decreasing for y.
An item costs y dollars and then a 20% discount is applied. Create an expression that could represent the price of the item after the discount. Explain your reasonin
An expression that could represent the price of the item after the discount is 0.8y.
Given that, an item costs y dollars and then a 20% discount is applied.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Cost price = $y and Discount percentage = 20%
Discount = 20% of y
= 20/100 × y
= 0.2y
The price of the item after the discount = y-0.2y
= 0.8y
Therefore, an expression that could represent the price of the item after the discount is 0.8y.
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Solve for U.
-3 + 2u + 6 = -8u - 7
What does U equal?
Answer:
U = -1
Step-by-step explanation:
Answer:
u=-1
Step-by-step explanation:
-3 + 2u + 6 = -8u - 7
2u-3+6=-8u-7
2u+3=-8u-7
we will collect like terms
2u+8u=-7-3
10u=-10
u=-1
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The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. Write the ratios as fractions in simplest form. Ratio (red to blue) of the perimeters: Ratio (red to blue) of the areas: pleas help
Answer:
5/8 and 25/64
in poker, 5 cards are randomly dealt from a standard deck of 52 cards. (a) how many poker hands contain cards that are all the same suit (this is called a flush)? (b) what is the probability of that all the cards in a poker hand are the same suit?
In probability , 5148 possible flushes in poker.
What is probability in math?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics refers to the study of events subject to probability.there are C(13,5) 5-card hands… i.e.
the number of combinations of taking 5 cards from 13 distinct cards.
But, since there are 4 suits, there are then 4*C(13,5) possible “flushes.”
Thus, there are 4*1287=5148 possible flushes in poker.
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12.8 = 4v solve for v
Answer:
v=3.2
Step-by-step explanation:
12.8 = 4v
v= 12.8/4 isolate the variable and divide.
v= 3.2 Answer
Please help!
6|x - 8| ≤ 12
x ≤ ?
x ≤ ?
Answer: 10, 6
Step-by-step explanation:
[tex]6|x-8| \leq 12\\\\|x-8| \leq 2\\\\-2 \leq x-8 \leq 2\\\\6 \leq x \leq 10[/tex]
Is y=6x proportional?
y = 6x is proportional.
Proportionality between x and y is defined if there is a constant of proportionality 'k' such that y = kx.
So here, the constant of proportionality in y = 6x is 6.
This equation also means that y varies directly with respect to x and then 6 is the constant of variation.
That is, y is directly proportional to x.
Then a change in y implies a corresponding change in x in the same direction as that of y.
If x increases, then y also increases and if x decreases, then y also decreases.
These changes are related to the constant of proportionality 6.
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Which list shows the values in order from least to greatest?
0-0.5
√(0.5)
0-0.5
20% √/0.5
○ 20% |−0.5| √/0.5
○ = √/0.5 |−0.5| 20%
20%
The values in order from least to greatest are 0-0.5,√(0.5),20%,20% √/0.5,√/0.5 |−0.5| 20%. we eliminate 0-0.5 because the value is two times in the option.
What is the percentage?Percentage represents a proportion or a fraction of a whole, expressed as a portion of 100. It is commonly denoted by the symbol "%" (percent), which literally means "per hundred."
According to the given information:
The values in the list are:
0-0.5 = a range of values from 0 to 0.5, inclusive
√(0.5) ≈ 0.7071
20% = 0.2
20% √/0.5 = 0.2 * √(0.5) ≈ 0.1414
√/0.5 |−0.5| 20% = √(0.5) * |−0.5| * 0.2 ≈ 0.0707
Therefore, the correct list in order from least to greatest is:
0-0.5
√(0.5)
20%
20% √/0.5
√/0.5 |−0.5| 20%
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I need to know how to rewrite the expression using the distributive property of multiplication over addition
Given the following expression:
[tex]\text{ 10(3 + 2)}[/tex]Rewriting this using the distributive property of multiplication over addition will be:
[tex]\text{ 10(3) + 10(2)}[/tex]Therefore, the answer is letter B - 10(3) + 10(2)
if luna adds 1/2 cups of flour to a mixing bowl for a recipe 5 times, how much flour has she added?
Answer:
10 cups
I hope this helps, have a great day/night!
What is the y intercept of the function shown?
Answer:
-2
Step-by-step explanation:
The line passes through the y-intercept at the point (0, -2)
DIVIDE THE POLYNOMIALS USING LONG METHOD. QUESTION 1 Divide (x4 + 2x³ - 13x² - 38x - 24) + (x + 4)
Answer:
QUESTION 1: x³ - 2 x² - 5 x - 18 remainder 48
Please answer all 3 questions in the photo for easy point! ( 30 points + Brainliest )
Answer:
6. a because a rectangle with sides 8 and 2 has a perimeter of 20 but its area is 16.
7. d because 4 is an even number and it is a perfect square.
8. b because a pen can be used to write but is not a utensil.
Step-by-step explanation:
Nina bought 1.725 pounds of pecans and 1.83
pounds of almonds. She also bought twice as many
pounds of walnuts as pecans. How many more
pounds of walnuts did she buy than almonds?
Nina bought 3.45 pounds of walnut.
Nina bought 1.62 pounds more walnut than almonds
Quantity of pecan bought by Nina = 1.725 pounds
Quantity of almonds bought by Nina = 1.83 pounds
The process of comparison of numbers establishes the similarities between two numbers and determines which number is greater, smaller, or equal to another number.
Quantity of walnuts = 2*Quanitity of pecans
= 2*1.725
= 3.45 pounds
So, she bought 3.45 pounds of walnut
Pounds of walnuts bought more than the almonds = Quantity of walnuts bought by Nina - Quantity of almonds bought by Nina
= 3.45 - 1.83
= 1.62 pounds
So, she bought 1.62 pounds more walnuts than almonds
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141% as a mixed or whole number
Answer:
1 41/100
Step-by-step explanation:
Answer:
141/100 (Already in simplest form). As a mixed number, it is: 1 41/100
Step-by-step explanation:
help me pls battery is low help
The solution to the system of linear equations 6 · x + 2 · y - 9 = 0 and y = 2 · x - 3 is (x, y) = (1.5, 0).
How to resolve a system of linear equations by graphic methods
In this question we find a system of two linear equations and two variables, this can be done by using a Cartesian plane and drawing each line equation. The solution to the system is represented by the point of intersection of the two lines.
Therefore, the solution to the system of linear equations is (x, y) = (1.5, 0).
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The solution to the system of linear equations will be; 6x + 2y - 9 = 0 and y = 2x - 3 is; (1.5, 0).
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
To solve a system of linear equations by graphic methods: we need a system of two linear equations and two variables, using a Cartesian plane and each line equation.
The solution to the system is shown by the point of intersection of the given lines.
6x + 2y - 9 = 0
y = 2x - 3
6x + 2 (2x - 3 ) - 9 = 0
x = 1.5
(x, y) = (1.5, 0).
Hence, the solution to the system of linear equations would be; (x, y) = (1.5, 0).
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Find (a) f(-8) and (b) f(3).
(a) f(-8)=
(b) f(3) =
Answer:
[a] 15
[b] 13
Step-by-step explanation:
We can use the visual diagram given to solve. We can see that when you input -8 (on the left side) the arrow leads to the output 15, our answer.
We use the same method for part b. When you input 3 (on the left side) the arrow points to 13 (on the right side) giving us an answer of 13.