Part A: Yes, there is a correlation between the number of hours students spent studying and the score on the music test because As we increase the hours of studying by 0.5 hours, then the music score increases by 2.
Part B: A function that best fits the data is; y = 60 + 4x
Part C: The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.
How to find the correlation of line of best fit?We have given the table below showing the data:
Number of hours spent studying (x) 0 0.5 1 1.5 2 2.5 3 3.5 4
Score on music test (y) 60 62 64 66 68 70 72 74 76
A) As we increase the hours of studying by 0.5 hours, then the music score increases by 2.
B) The function which best fits the data for the correlation from the above is; y = 60 + 4x
C) The slope and y-intercept of the plot indicates that Y is the score obtained in music test and number of hours spent on studying.
The slope of the above equation represents the rate of increase in music score with respect to an increase in the number of hours spent on studying.
The y-intercept gives the music score when the number of hours spent on studying is zero.
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write an expression as a number in scientific notation
(7 x 10³)(5.4 x 10⁴)/ 9 x 10² ?
4.2x10¹⁰
3.4x10¹⁰
4.2x10⁵
3.4x10⁵
The given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.
According to the question.
We have an expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10².
Since, we have to write the above expression as a number in scientific notation.
As we know that, scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
Thererefore, the expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation
(7 x 10³)(5.4 x 10⁴)/ 9 x 10²
= (7 × (10^7) × 54)/ 9 × (10^2) × 10
= 7 × 6 × 10^(7 - 3)
= 42 × 10^4
= 4.2 × 10^5
Hence, the given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.
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Find the remaider theorem of (x^3-6x^2+x-5) by x+2
Answer:
-39Step-by-step explanation:
x³-6x²+x-5
but it is divided by x+2
x+2=0.
x=-2.
(-2)³-6(-2)²+(-2)-5.
-8-6*4-2-5.
-8-24-7
-15-24
-39how do you solve
7 - 5/7 =
Step-by-step explanation:
by bringing all terms to the same fractions (with the same denominator).
so, we have
7
5/7
that means we want to bring both numbers to .../7 form.
7 means 7 whole units.
1 whole unit has now many parts ?
if we aim for 2 parts, that makes 1 whole unit 2/2.
if we aim for 3 parts, 1 whole unit is 3/3.
...
you see, 3/3 = 1/1 = 1.
that is the whole trick.
so, we are looking for 7 parts, and 1 whole unit is 7/7.
now we have 7 whole units.
how many parts are those ?
well, 7 × 7/7 = 49/7
there we go.
we have
7 - 5/7 = 49/7 - 5/7 = 44/7 = 42/7 + 2/7 = 6 2/7
What’s is 365x4 area model
Answer:
365 x 4 = 1460
Step-by-step explanation:
The area model shows that 365 multiplied by 4 is equal to 18.
First, we draw a rectangle to represent the number 365. We divide it into three parts vertically to represent the digits 3, 6, and 5.
3 6 5
Next, we draw a rectangle to represent the number 4. We position it to the right of the rectangle for 365.
3 6 5
4
To find the area, we calculate the individual areas of each section and then add them up.
The area of the rectangle representing 3 is 3 times the height, which is 1.
3 6 5
| | |
| | |
| | |
The area of the rectangle representing 3 is 3.
The area of the rectangle representing 6 is 6 times the height, which is 1.
3 6 5
| | | |
| | | |
| | | |
The area of the rectangle representing 6 is 6.
The area of the rectangle representing 5 is 5 times the height, which is 1.
3 6 5
| | | | |
| | | | |
| | | | |
The area of the rectangle representing 5 is 5.
The area of the rectangle representing 4 is 4 times the height, which is 1.
3 6 5
| | | | | |
| | | | | |
| | | | | |
So, the area of the rectangle representing 4 is 4.
Now, the total area, we add up the areas of the individual sections:
= 3 + 6 + 5 + 4
= 18
Therefore, the area model shows that 365 multiplied by 4 is equal to 18.
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The average worker in a manufacturing plant produces 27 units every hour the manager of the plant took a sample of 25 workers and gave them special training designed to increase their productivity after the special training was complete the 25 workers produced 28.2 units every hour with stand deviation of 2.9 what is the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher
The probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.
How to illustrate the information?It should be noted that from the information, after the special training was complete the 25 workers produced 28.2 units every hour with stand deviation of 2.9.
Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher will be:
= 1 - P[(Z (28.2 - 27)/29/✓25)]
= 1 - P(Z < 2.07)
It should be noted that this will be looked on the distribution table.
= 1 - 0.9808
= 0.0192
Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.
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HELP! The problem's in the image, if you can't see it tell me.
Answer:
x/(1-x)
Step-by-step explanation:
We start by induction. The first 2 terms are x/(1-x^2) and x^2/(1-x^4), respectively. When we add them together using special factorizations, we get: (x^3+x^2+x)/(1-x^4). We quickly realize that the numerator is a geometric series. Applying the following formula, we can simplify our expression to (x^4-x)/(1-x^4)(x-1). Now, we introduce our 3rd term, and add that to our sum. That gets us: (x^7+x^6+...+x)/(1-x^8). This is another Geometric series, and we apply the exact same formula, for this new fraction: (x^8-x)/(1-x^8)(x-1). We realize this is a pattern, and we can utilize this pattern for the sum of the first n terms.
We look at the exponents. For the first 3 terms, the Degree is 8, for the first 2 terms, the Degree is 4. We take note that this looks like x^2^n.
Using that our general formula IS: (attached to this text) (x^2^n-x)/(1-x^2^n)(x-1). Now, when 0<x<1 and n approaches infinity, what do we get?
all terms x^2^n are so small, it's basically redundant, and can be crossed off. This leaves us with -x/(x-1), which can be simplified to x/(1-x).
Select all that apply
A. The slope of m is -2/5
B. The slope of q is -5/2
C. The slope of n is 2/5
D. The slope of p is -5/2
Can you please explain how you solve it?
Answer:
C is correct! for the slope, N is represented.
Step-by-step explanation:
The slope of the line that contains the points (1, 9) and (3, 4) is 4−93−1=−52.
slope=y2−y1x2−x1=4−93−1=−52
The negative reciprocal is 25, which is the slope of the perpendicular line.
Mr John withdrew some money from the Bank. He gave 1 to his son and 1/3 to his daughters.
1)If he had 500.00ghs left,how much did he take from bank
2)what is the percentage of the money his daughters received?
Answer:
www
Step-by-step explanation:
www
In the figure below, h
o. Find the values of X and z.
Applying the same-side-interior angles theorem, the values are:
x = 95°
z = 35
What is the Same-Side-Interior Angles Theorem?An examples of angles that are referred to as same-side-interior angles are x° and 85°.
According to the same-side-interior angles theorem, the sum of x and 85 will give 180 degrees if lines h and o are parallel to each other.
Since h║o, therefore:
x + 85 = 180
x + 85 - 85 = 180 - 85
x = 95°
(6z - 115)° and x° are vertical angles, therefore:
6z - 115 = x
Plug in the value of x
6z - 115 = 95
6z - 115 + 115 = 95 + 115
6z = 210
6z/6 = 210/6
z = 35
Thus, applying the same-side-interior angles theorem, the values are:
x = 95°
z = 35
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Solve the equation m² = 14. Lesson 1-5
Answer:
m=√14,−√14
Decimal Form:
m=3.74165738, -3.74165738
Step-by-step explanation:
[tex]q=4h+4w solve for h[/tex]
Answer:
w-q=h
Step-by-step explanation:
4w-q=4h
4w/4-q=4h/4
w-q=h
Meghan is spending money at a constant rate. Suppose she initially has $1100, and after 4 months, she has $720. Which of these expresses the rate at which Meghan's amount of money is changing?
In linear equation, 95 is Meghan's amount of money is changing .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Based on the given conditions, formulate ( 1100 - 720 ) ÷ 4
Calculate the sum or difference = 380/4
Cross out the common factor = 95
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The sets and are given below.
, , , , ,
, , , , ,
Find the intersection of and .
Find the union of and .
Write your answers using set notation (in roster form).
The intersection of M and F is {d}.
The union of M and F is {b, d, e, h, j}
What is the union and the intersection?A set is a collection that is used to model a collection of different things. A set can be described as a collection of objects whose elements are fixed and cannot be changed.
To write a set in a roster form, the elements in the set are written in a row within curly brackets - { }. The elements in the set would be separated by commas.
The intersection represents only elements that are common to two or more sets. Th sign used to represent intersection is ∩. The union of sets are all the elements in the set. The sign used to represent union is U.
The intersection of M and F = d.
It is only d that is in both set M and set F.
The union of M and F = {b, d, e, h, j}
Here is the complete question:
The sets M and F are given below.
M= ( b, d, h)
F= (d, e, j)
find the union of M and F. Find the intersection of M and F.
Write your answers using set notation (in roster form).
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What is the value of y3x if y=3 and x=7
Y3x=
Answer: {y,x} = {-9,-2}
Step-by-step explanation:
3^2 x 3
pls help i can figur it out
Answer: 27
Step-by-step explanation:
3^2 = 3 x 3= 9
9 x 3 = 27
The packaging of a thermometer claims that the thermometer is
accurate within 1.5 degrees of the actual temperature in degrees Fahrenheit.
Write and solve an absolute value equation to find the least and greatest
possible temperature if the thermometer reads 87.4° F.
The required absolute value equation is |x - 87.4| = 1.5
Also, if the thermometer reads 87.4° F, the least possible temperature is 85.9° F and the greatest possible temperature is 88.9° F
In this question, the thermometer is accurate within 1.5 degrees of the actual temperature in degrees Fahrenheit.
We need to find the least and greatest possible temperature if the thermometer reads 87.4° F
Let x be the temperature in degrees Fahrenheit.
From given information, an absolute value equation would be,
|x - 87.4| = 1.5
We know that, | ±a | = a
x - 87.4 = ±1.5
Case 1: x - 87.4 = 1.5
x = 1.5 + 87.4
x = 88.9° F
Case 2: x - 87.4 = -1.5
x = -1.5 + 87.4
x = 85.9° F
Therefore, the required absolute value equation is |x - 87.4| = 1.5
Also, if the thermometer reads 87.4° F, the least possible temperature is 85.9° F and the greatest possible temperature is 88.9° F
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What is the ruler postulate?
The distance between two points can be determined by the
the absolute value of the difference
of the real number values of the two points.
OR
What is the ruler postulate?
The distance between two points can be determined by the
the sum
of the real number values of the two points.
or
What is the ruler postulate?
The distance between two points can be determined by the
the absolute value of the sum
of the real number values of the two points.
or
What is the ruler postulate?
The distance between two points can be determined by the
the difference
of the real number values of the two points.
The ruler postulate is that A. the distance between two points can be determined by the absolute value of the difference of the real number values of the two points.
What is the ruler postulate?The set of points on a line can be arranged in such a way that the set of real numbers and the set of points correspond exactly, and the distance between any two points is equal to the absolute value of the difference between the corresponding numbers.
Therefore, the ruler postulate is that the distance between two points can be determined by the absolute value of the difference of the real number values of the two points.
In conclusion, the correct option is A.
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there is 5 days in a school week. there is 6 dollars in a lunch account. 94 dollars is added to the account so now it is a hundred. school lunch cost three dollars everyday. How long will it take to exhuast the money.
The time taken to exhaust the money will be 33 days.
How to calculate the value?Total amount = 100
Let the number of days be represented by x.
Therefore, the appropriate expression will be:
(3 × x) = 100
3x = 100
Divide
x = 100/3
x = 33.33
Therefore the time taken will be 33 days.
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Eliana is playing a card game with her cousins. At the start of this turn, she had −12 points in the game. On this turn, she gets 7 points. What sum could be calculated to find the number of points Eliana now has?
________
Answer:
Step-by-step explanation:-12+7=-5
fdfdfsdzxvfdxcfdxcfcxf
Answer:
A
Step-by-step explanation:
95 [tex]\leq[/tex] 3.99s + 15.20
-15.20. -15.20
79.80 [tex]\leq[/tex] 3.99s
/ /
3.99 3.99
20 [tex]\leq[/tex] s
How much external financing will Tobin Supplies Company have to seek? Assume there is no increase in liabilities other than that which will occur with the external financing.
The amount of external financing Tobin Supplies Company have to seek assume there is no increase in liabilities other than that which will occur with the external financing is $58,250
What is the appropriate formula for external financing?
The formula that models the amount of external financing Tobin supplies company requires is a function of its increase in assets minus the retained earnings which would be used to part-fund the increase in assets
external funds needed=increase in assets-retained earnings
increase in assets=$105,000
retained earnings=net income-dividends
net income=sales*profit margin
net income=$550,000*10%
net income=$55,000
dividend payout ratio=15%
dividends=$55,000*15%
dividends=$8250
retained earnings=$55,000-$8250
retained earnings=$46,750
external funds needed=$105,000-$46,750
external funds needed=$58,250
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An engineering school reports that 52% of its students were male (M), 33% of its students were between the ages of 18 and 20 (A), and that 22% were both male and between the ages of 18 and 20.
What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M).
Your answer should be given to two decimal places.
point(s) possible
The total (after-tax) cost of a laptop computer is $1605.96. The local sales tax rate is 7.1%. What is the retail (pre-tax)
price?
Answer:
1491.94
Step-by-step explanation:
7.1/100 = x/1605.96
=114.02
1605.96-114.02=1491.94
HELP 50 POINTSThe stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008. What is the best prediction of the population in the year 2013?
The best prediction of the population in the year 2013 is 3541 based on the fact that the population decreases by 1.4% every year
What is the number of years between 2008 and 2013?
The number of years between 2008 when the population figure was at 3,800 and 2013 is 5 years, hence when determining the population for the year 2013 we need to bear in mind that the population has decreased by 1.4% over a period of 5 years
FV=PV*(1-r)^N
FV= best prediction of the population in the year 2013
PV=population in 2008=3800
r=decreasing rate of the population=1.4%
N=number of years that have passed between 2008 and 2013
FV=3800*(1-1.4%)^5
FV=3541
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Enter your answer in interval notation.
Enter any values to one decimal place.
To enter ∞ , type infinity. To enter ∪ , type U.
Answer:
(-4;2)
Step-by-step explanation:
The graph show us line on the -4 and 2 and I think the answer us (-4;2)
Negative two is equal to x divided by the sum of x and five
Shown in pic
Source: Trust me
This is the graph of y= x2 + 4x + 7 what is the range of this function?
The range of the function y = x^2 + 4x + 7 is y >= 3
How to determine the range of the function?The equation of the function is given as
y = x^2 + 4x + 7
Start by differentiating the above function
So, we have
y' = 2x + 4
Set the above equation to 0
So, we have
2x + 4 = 0
Divide through the equation by 2
So, we have
x + 2 = 0
Evaluate the like terms:
x = -2
Substitute x = -2 in y = x^2 + 4x + 7
y = (-2)^2 + 4(-2) + 7
Evaluate the expression
y = 3
The leading coefficient of the equation y = x^2 + 4x + 7 is positive
This means that the vertex is a minimum
So, the range is
y >= 3
Hence, the range of the function y = x^2 + 4x + 7 is y >= 3
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270 Calories in 3 servings; 450 Calories in 5 servings.
Answer:270 calories in 3 servings; 450 calories in
5 servings.
270 ÷3 90 450 ÷ 5 90
3 ÷3 1 5 ÷ 5 1
The unit rates are the
same so they are equal.
hope it helps! :)
(x+8)^2-43=-38
Solve for all values of x in simplest form
Answer:
x = √(5) - 8
x = -√(5) - 8
Step-by-step explanation:
Let's solve the problem,
→ (x+8)² - 43 = -38
→ x² + 64 - 43 = -38
→ x² + 21 = -38
→ x² = -38 - 21
→ x = √(-59)
→ [ x = √(5) - 8 ]
(or) [ x = -√(5) - 8 ]
Hence, it is the value of x.
LESSON 7.1 Geometry HELPPPPPPPP!!!!!!!!!!!!!!
1. Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
2. Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
3.Find the missing side of each triangle. Leave your answers in simplest radical form.
4.Find the missing side of each triangle. Leave your answers in simplest radical form.
1. The missing side of triangle is 10 CM
2. The missing side of triangle is 13 mi
3. The missing side of triangle is 3[tex]\sqrt{2}[/tex] mi
4. The missing side of triangle is [tex]\sqrt{219}[/tex] yd
The Pythagoras theorem equation is expressed as, , [tex]c^{2}[/tex]=[tex]a^{2}[/tex]+[tex]b^{2}[/tex], where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
We have different right triangles and their measurements.
we have to find the missing side of triangle.
The Pythagoras theorem equation is expressed as, [tex]c^{2}[/tex]=[tex]a^{2}[/tex]+[tex]b^{2}[/tex]
1. For diagram 1,
Let the length c=x,
a=6
b=8
then according to the Pythagoras theorem.
⇒[tex]x^{2}[/tex]=[tex]6^{2}[/tex]+[tex]8^{2}[/tex] ⇒ [tex]x^{2}[/tex]= 36+64=100
⇒x=10
therefore missing side of triangle is 10 CM
2. For diagram 2,
Let the length c=x,
a=5
b=12
then according to the Pythagoras theorem.
⇒[tex]x^{2}[/tex]=[tex]5^{2}[/tex]+[tex]12^{2}[/tex] ⇒ [tex]x^{2}[/tex]= 25+144=169
⇒x=13
therefore missing side of triangle is 13 mi
3. For diagram 3,
Let the length c=x,
a=3
b=3
then according to the Pythagoras theorem.
⇒[tex]x^{2}[/tex]=[tex]3^{2}[/tex]+[tex]3^{2}[/tex] ⇒ [tex]x^{2}[/tex]= 9+9=18
⇒x=3[tex]\sqrt{2}[/tex]
therefore missing side of triangle is 3[tex]\sqrt{2}[/tex] mi
4. For diagram 4,
Let the length a=x,
c=16,
b=[tex]\sqrt{37}[/tex]
then according to the Pythagoras theorem.
⇒[tex]16^{2}[/tex]=[tex]x^{2}[/tex]+[tex](\sqrt{37} )^{2}[/tex] ⇒ [tex]x^{2}[/tex]= 256-37=219
⇒x=[tex]\sqrt{219}[/tex]
therefore missing side of triangle is [tex]\sqrt{219}[/tex] yd
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