The value of the independent variable does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.
What is an independent variable?An independent variable can be defined as the variable that is being manipulated, controlled, and which varies in an experimental or research study for the exploration of its effects.
It is termed “independent” because it's not affected or changed by other variables in an experiment or study.
It is known as a variable that is unaffected in a function and cannot be determined by the other variables in that function.
Other names for an independent variable includes;
Explanatory variableInput variableExposure variableControlled variablePredictor variableHence, the variable is independent.
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1.
find a
a =
21°
explain why using one of these
words: adjacent,
complementary, supplementary,
vertical
explanation goes here
add a pic of your work
(or just type it here)
to show HOW you got your
answer
pic (or typing) goes Hereford
[tex]21+a=90 \implies a=69^{\circ} [/tex]
This is because the angles are complementary.
Amy is experimenting with three different strawberry smoothie recipes. She makes all three smoothies for each of her x friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6. Pick all the expressions that represent how many strawberries Amy needs for all the smoothies.
The total number of strawberries needed for making all the smoothies can be represented by the expression -
y = 15x
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Amy who is making all three smoothies for each of her x number friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6.
Number of friends [n] = x
Each of the three friends will get smoothies made from recipe 1, recipe 2 and recipe 3.
Then -
Number of strawberries needed for smoothie made from recipe 1 for x friends = n[1] = 4x
Similarly, for smoothies made from recipe 2 and 3 will need -
n[2] = 5x and n[3] = 6x number of strawberries.
Assume that total number of strawberries needed for making all the smoothies are y. Then, we can write -
y = 4x + 5x + 6x
y = 15x
Therefore, the total number of strawberries needed for making all the smoothies can be represented by the expression -
y = 15x
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PLEASE ANSWER QUICK ILL GIVE BRAINLIEST IF CORRECT
Answer:
domain: [-1,4]
range: [-2,4]
the graph is not a function, this is proven by using the vertical line test.
hope this helps :)
solve the system of equations using the elimation menthod. show your work. make sure to express your solution as an ordered pair
-3x - 4y = -5
12x - 3y = -18
Multiply the first equation by 4, and add both
-12x - 16y = -20
+
12x - 3y = -18
___________
-19y = -38
Solve for y:
y = -38/-19
y= 2
Replace y on any equation and solve for x
-3x - 4(2)=-5
-3x -8 = -5
-3x = -5+8
-3x = 3
x=3/-3
x=-1
Solution = (-1,2)
Each letter is three. 5 m away from the base of the building. How high is window A?
Solution
A
Using pythagorean theorem
[tex]\begin{gathered} 5.5^2=3.5^2+A^2 \\ 30.25=12.25+A^2 \\ Re-arrange \\ A^2=30.25-12.25 \\ A^2=18 \\ Take\text{ the square root of both sides} \\ A=\sqrt{18} \\ A=4.2426 \end{gathered}[/tex]The final answer
The height of window A is
[tex]4.24meters[/tex]
State the postulatr ir theorem for no. 6 and 9
Solution
Number 6
for this case we can see that we have two common angles and one equal side. By the way we have also a common side and then since we have right triangles the correct postulate would be:
SSS
Number 9
Select the correct answer.
How many solutions for x does the following equation have?
2(x+4) -1 = 2x + 7
O A. 1
О в. о
OC. 7
OD. infinite
Answer:
D. infinite
Step-by-step explanation:
2(x+4) -1 = 2x + 7
To solve for x
Distribute
2x+8 -1 = 2x+7
Combine like terms
2x +7 = 2x + 7
Subtract 2x from each side
2x+7-2x = 2x+7-2x
7 = 7
This is always true, so there are infinite solutions
The actual lengths of Wall A, Wall B, and Wall D are 2.5 m, 2.75 m, and 3.75 m. If 1 m = 4 cm then determine how long these walls will be on Noah’s scale drawing. Be sure to include your units; use 'cm' for centimeters.
Step-by-step explanation:
1 m = 4 cm
therefore,
A = 2.5 m = 2.5×1 m = 2.5×4 cm = 10 cm
B = 2.75 m = 2.75×1 m = 2.75×4 cm = 11 cm
D = 3.75 m = 3.75×1 m = 3.75×4 cm = 15 cm
Does the table show a proportional relationship? If so, what is the value of y when x is 11?
x 4 5 6 10
y 64 125 216 1,000
The original price of a DVD is $12 the sale Price is 35% of the original price final total cost of the DVD
Answer: $4.20
Step-by-step explanation:
The sale price is $12 * .35 = 4.2
A department store is having an after-Christmas sale in which
coats are discounted 30% and suits are discounted 25. If Joe
purchases a coat that was originally $300 and a sair that was
originally $400, how much money did he spend
In total, he spend $510 after discount.
What is discount?A deduction taken from the gross amount or worth of anything, such as a price decrease made from the standard or list price, giving clients a 10% discount to purchase tickets. A proportionate withdrawal from a loan account, typically done in exchange for cash or quick payment.
Given Data
Coats are discounted 30%
Suits are discounted 25%
Joe purchased a coat of $300
= 300 - [tex]\frac{30}{100}[/tex] × 300
= 300 - 90
= 210
He purchased coat for $210.
He purchased a suit $400.
Suits are discounted 25%
= 400 - [tex]\frac{25}{100}[/tex] × 400
= 400 - 100
= 300
He purchased suit for $300.
In total, he spend $510 after discount.
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In a class there are
10 students who play football and cricket
7 students who do not play football or cricket
14 students who play football
21 students who play cricket
Find the probability that a student chosen at random plays football and cricket.
Answer: 31.25%
Step-by-step explanation:
Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%
1/4(n-6)=1/4n-3/2
Hint: undo the fraction
The solution to 1/4(n - 6) = 1/4n - 3/2 is infinite many solutions
How to solve the equation?The equation is given as
1/4(n - 6) = 1/4n - 3/2
Multiply through the fraction equation by 4
So, we have the following equation
4 x 1/4(n - 6) = 4 x 1/4n - 4 x 3/2
Evaluate the products in the equation
So, we have the following equation
n - 6 = n - 6
Evaluate the like terms
0 = 0
The equation cannot be solved further
If the solution to an equation is 0 = 0, then the equation has infinite many solutions
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Answer: infinite many answers
Step-by-step explanation:
What is the value of 2x + 11y when x = 4 and y = 2? 303848136
We want to find the value of the expression;
[tex]2x+11y[/tex]When x = 4 and y = 2.
All we have to do is substitute these values; when we do that, we have;
[tex]\begin{gathered} 2(4)+11(2) \\ =8+22 \\ =30 \end{gathered}[/tex]Therefore, the answer is 30.
how many 14 goes into 78
The amount of times that 14 goes into 78 is; 5 times
How to carry out division of numbers?
We want to find how many 14 goes into 78.
Now, it is pertinent to note that this expression is used in our common daily lives for basic things of life. For example, if i want to know how many 10 dollars can go into 100 dollars, i will just divide 100 by 10.
Similarly another example is if i want to know how many 5 liters container of fuel would go into a 60 liters tank, i will just divide 60 by 5 to get the number.
In a similar vein, we can solve this question by dividing 78 by 14 to get;
78/14 = 5 ⁸/₁₄
This means 14 can only go in 5 full times as we will not count the fraction.
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Suppose that the mean cranial capacity for men is 1160 cc (cubic centimeters) and that the standard deviation is 200 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements.
Solution:
Given;
[tex]\mu=1160,\sigma=200[/tex]The z-score is calculated using;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{760-1160}{200}\text{ at }x=760 \\ \\ z=-2 \\ \\ z=\frac{1560-1160}{200}\text{ at }x=1560 \\ \\ z=2 \end{gathered}[/tex]Thus;
[tex]P(-2ANSWER: 95%(b) The z-score of 99.7 probability is between -3 and 3. Thus;
[tex]\begin{gathered} -3=\frac{x_1-1160}{200} \\ \\ x_1=560 \\ \\ 3=\frac{x_2-1,160}{200} \\ \\ x_2=1760 \end{gathered}[/tex]ANSWER: Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc
If x=8, y=4 z=2 then what is 3z(x-z)-y(x/2)
x ÷ 5 - 13 = 2
What is x?
Answer:
75
Step-by-step explanation:
Answer:
75. ..... ............................
Kaj earns $35 for 2 hours of work. If she makes a constant hourly wage, which table
represents the relationship between the number of hours she works and her total
earnings?
The table of values of the relationship between time and earnings is a linear relation
How to determine the table of values that represents the earnings?From the question, we have the following parameters:
Number of hours = 2 hours
Total earnings in this time = $35
Also from the question, we understand that:
She makes a constant hourly wage
A constant hourly wage implies that the table of values has a linear relationship
In this case, the linear relationship is represented as
A(t) = constant hourly wage * t
Where
A(t) represents the earnings
t represents the number of hours
So, we have
constant hourly wage * 2 = 35
Divide both sides of the equation by 2
So, we have
constant hourly wage = 17.5
Substitute constant hourly wage = 17.5 in A(t) = constant hourly wage * t
A(t) = 17.5 * t
Evaluate
A(t) = 17.5t
Using the values of t as:
t = 0, 2, 4, 6
We have the following table of values
Number of hours (t) || Amount earned
0 0
2 35
4 70
6 105
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f(x) = -x² + 8x - 12; Find ƒ(3)
The result of the function f(3) is 3.
What does it mean to evaluate function?The process of evaluating a function is typically straightforward when we have the function in the form of a formula. When a function is evaluated, a variable is replaced with its provided value or expression. Example. For x = 5, evaluate f(x) = 2x + 4. This implies to simplify and change x to 5. It is advised to enclose the value being substituted in parentheses.Given:
f(x) = -x² + 8x - 12
x = 3
Putting the value of x in the given function to obtain the outcome of the function,
f(3) = -(3)² + 8 × 3 - 12
= -9 + 24 - 12
= 24 - 21
= 3
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Help on math problem precalculus
Remember that the domain is the numbers that x can take
x=5 has a domain of only 5
y = 1/x cannot have a value of x=0 because 1/0 is undefined
t = sqrt(x) cannot have negative values because sqrt( negative numbers) is not defined in the real number system
y = |x| is defined for all values of x so it has a domain of all real numbers
Needing help for this
The pairs of angles that are linear pairs involving point F are:
A. ∠DFC and ∠CFG
D. ∠HFD and ∠CFD
E. ∠GFH and ∠GFC
F. ∠HFG and ∠DFH
What is a Linear Pair?When two angles that are adjacent to each other, (that is, they share the same vertex and the same side), are located on a straight line, these angles are linear pairs and are also supplementary angles.
Making reference to the image given, angles DFC and CFG share a common vertex F and a common side CF. Also, they lie on a straight line. Therefore, angle DFC and angle CFG are a linear pair.
Angles HFD and CFD share a common vertex F and a common side FD. They lie on a straight line. Thus, angle HFD and angle CFD are also a linear pair.
The same thing applies to angle GFH and angle GFC, as well as angle HFG and angle DFH.
The linear pairs are:
A. angle DFC and angle CFG
D. angle HFD and angle CFD
E. angle GFH and angle GFC
F. angle HFG and angle DFH
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Consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. All angles are right angles. Which plane(s) contain point B and appear to be parallel to plane CDH?
The plane containing point B and parallel to the plane CDH is plane ABF.
What is defined as the parallel plane?Parallel planes are spatial planes that never intersect. The length about any line segment perpendicular both to planes connecting two parallel planes is indeed the distance between them. There are an infinite number of perpendicular line segments between two parallel planes. Two of the perpendicular segments the above are line segments AB and CD. Any line segment that is perpendicular to both planes also has the shortest distance between them.As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.
But plane ABC is intersecting the given plane CDH, while plane ABF is not.
Thus, plane ABF is parallel to the plane CDH.
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A college professor hands out a list of 16 questions, 8 of which will appear on the final examination for the course. One of the students taking the course is pressed for time and can prepare for only 9 of the 16 questions on the list. Suppose the professor chooses the 8 questions at random from the 16. What is the probability that the student will be prepared for exactly 4 questions?
The probability that the student will be prepared for exactly 4 questions is; 0.3427
How to solve Hypergeometric Probability distribution?
Hypergeometric distribution is defined as a discrete probability distribution that expresses the probability of k successes in n draws, done without replacement, from a finite population of size N that contains exactly K objects with that feature. In this disdtribution, each draw is either a success or a failure.
The probability mass function of Hypergeometric distribution is given by the formula;
P(K = k) = KCk * N-KCn-k ]/NCn
Now, the probability that the student will be prepared for exactly 4 questions will be;
P(K = 4) where;
N = 16
K = 9
n = 8
Solving P(K = 4) = 9C4* 16-9C8-4 ]/16C8 = 0.3427
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What is 50% of 100%?
Answer:
We need to determine 50% of 100 now and the procedure explaining it as such
Step 1: In the given case Output Value is 100.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 100 = 100%.
Step 4: In the Same way, x = 50%.
Step 5: On dividing the pair of simple equations we got the equation as under
100 = 100% (1).
x = 50% (2).
(100%)/(x%) = 100/50
Step 6: Reciprocal of both the sides results in the following equation
x%/100% = 50/100
Step 7: Simplifying the above obtained equation further will tell what is 50% of 100
x = 50%
Therefore, 50% of 100 is 50
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1. A triangle is rotated 90° about the origin. What is true about the relationship between the image and the
pre-image?
(1 point)
The lengths of the sides and the measures of the angles are preserved, so the triangles are congruent.
The lengths of the sides are enlarged and measures of the angles are preserved, so the triangles are similar.
The lengths of the sides change and the measures of the angles change as well, so the triangles look nothing alike.
The lengths of the sides are reduced and measures of the angles are preserved, so one triangle is a reduction of the other.
Answer:
the first answer option : all lengths and angles stay the same.
Step-by-step explanation:
imagine you have a piece of plastic or glass of a triangular shape on your table.
now, lower your hand on the table, so that your thumb touches the table and one of your other fingers touches the triangle on the top.
and now twist your hand that your thumb stays at the same point, and your finger holding the triangle starts making a circular motion.
that finger is dragging the triangle along.
what happens to the triangle ? it keeps its original shape, and changes only its location and orientation.
that is what a rotation is.
Find a function f whose graph is a parabola with the given vertex and that passes through the given point.
vertex (−1, 9); point (−2, −8)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=9 \end{cases}\implies y=a(~~x(-1)~~)^2 +9\implies y=a(x+1)^2 + 9 \\\\\\ \textit{we also know that} \begin{cases} x=-2\\ y=-8 \end{cases}\implies -8=a(-2+1)^2 + 9 \\\\\\ -17=a(-1)^2\implies -17=a\hspace{9em}\boxed{y=-17(x+1)^2 + 9}[/tex]
Solve. 5(y - 10) = -5 Answer: Submit Answer att
We divide both sides by 5 so we can eliminate the parenthesis:
[tex]\begin{gathered} 5(y-10)=-5 \\ \frac{5(y-10)}{5}=-\frac{5}{5} \\ y-10=-1 \end{gathered}[/tex]Step 2We rearrange the terms so the terms with the unkown variable y are on the left side and the other ones on the right side:
y - 10 = -1
↓ adding 10 both sides
y - 10 + 10 = -1 + 10
y + 0 = 9
y = 9
Answer: y = 9Help Me Pleaseeeeeee.
Based on the dimensions of the right triangle, the equation to be used to find the missing lengths is hypotenuse² = Known leg² + Unknown leg².
How to find a missing length on a right angled triangle?To find the missing length of a right-angled triangle, you should use Pythagoras theorem.
This theorem allows you to find the dimensions of missing leg as:
hypotenuse² = Known leg² + Unknown leg²
When you solve for the missing length, the length is:
9² = 6² + Unknown leg²
81 = 36 + Unknown leg²
Unknown leg² = 81 - 36
Unknown leg = √(81 - 36)
Unknown leg = 6.7
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In a poll, 1,004 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 48% said that they were in favor. Identify the population and the sample.
Question content area bottom
All adults in the country and considered as population. 1003 men in the country are adults that are selected.
What is sample?Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
Given Data
In a poll, 1,004 men in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, 48% said that they were in favor.
1)Population
All adults in the country and considered as population.
2) Sample is
1003 men in the country are adults that are selected.
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