Step-by-step explanation:
Given,
Kente invested part of money for 2 yr in stock fund that earned the equivalent of 6.5 % simple interest.He put remaining money in a 18 month certificate of deposit that earn of 6.5%simple interest.
Let he invested in stock fund be$ x. Remaining money =$(8000-x)
∴He got interest from stock fund was = [tex]\frac{PRt}{100}[/tex]
=$[tex]\frac{x\times6.5\times2}{100}[/tex] [here P =x , R = 6.5% and t = 2 yr]
=$ [tex]\frac{{13 x}}{{100} }[/tex]
Again he got interest from deposit was = [tex]\frac{PRt}{100}[/tex]
=$ [tex]\frac{(8000-x)\times 2.5\times\frac{18}{12} }{100}[/tex] [here P = (8000-x), R=2.5% and t =[tex]\frac{18}{12} yr[/tex]]
=$ [tex]\frac{(8000-x) \times 7.5}{200}[/tex]
According to problem
[tex]\frac{{13 x}}{{100} }+\frac{(8000-x) \times 7.5}{200}= 855[/tex]
⇔[tex]\frac{26x + 60000 - 7.5}{200} =855[/tex]
⇔18.5 x =171000 - 60000
⇔x = [tex]\frac{11100}{18.5}[/tex]
⇔x = 6000
So he invested in stock fund was = $6000
and in certificate of deposit was =$(8000- 6000)= $ 2000
Select the answer with the correct number of significant figures for each calculation. (6.022 × 10^23) × 2.58 = 1.55 × 10^24 1.554 × 10^24 1.5537 × 10^24
Answer:
1.55 × 10^24
Step-by-step explanation:
The answer is A aka 1.55 x 10 to the power of 24
A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.
f(x) = Left-bracket StartFraction x Over 10 EndFraction right-bracket
Which describes the meaning of f(x)?
Answer:
A customer earns one free night per 10 nights stayed.
Step-by-step explanation:
A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.
Here, [tex]f(x) = \frac{x}{10}[/tex] ........... (1)
In the above equation if we put x = 10 nights then f(10) = 1 night.
From, the equation (1) we get that a customer earns one free night per 10 nights stayed. (Answer)
The correct option is A. a customer will earn 1 free night per 10 night stayed.
Given,
[tex]f(x)=\dfrac{x}{10}[/tex]..........equation (1) .
Since the hotel offers a reward program based on the number of nights stayed. The function [tex]f(x)[/tex] represents the number of free nights earned as a function of [tex]x[/tex], the number of nights stayed.
From equation (1), it is clear that f(x) is the one- tenth times of x. it means the customer will earn 1 free night per 10 night stayed.
Hence the correct option is A. a customer will earn 1 free night per 10 night stayed.
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Miguel and Molly are cyclists. The graph shows the distance Miguel biked one day. Molly biked at a rate of 0.15 mile per minute. Which statement about their speed is true? Why
Answer:
Miguel traveled 0.2 mile per minute.
Step-by-step explanation:
3÷15=0.2
Speed can be interpreted from a graph's slope in a distance versus time plot. Comparing this to Molly's speed of 0.15 mile per minute, we could establish who is faster or slower. However, without the actual graph of Miguel's bicycling, we can't make a specific comparison.
Explanation:This question relates to graph interpretation and the concept of speed. Here, we're trying to compare the cycling speed of Miguel and Molly. Molly's speed is given as 0.15 mile per minute. Without the graph available, we cannot definitively compare their speeds. But let's briefly explain what we'd look for.
If we had Miguel's graph, we'd specifically examine the slope of the graph. In a distance vs. time plot, speed is represented by the slope of the graph. Therefore, if the slope of Miguel's graph indicated a value higher than 0.15 mile per minute (steep slope), Miguel was going faster. Conversely, if it showed a lesser value (gentle slope), Miguel was going slower.
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Please help I need your it please
The following graph, made by the manager of the basketball team, compares the free throw percentages for various players.
Which statement best describes why this graph could be misleading?
A.The graph does not indicate if the free throws were made at home or away.
B.The color of the bar for Player H is different from the color of the other bars in the graph.
C.The graph is missing the scale on the y-axis, making it unclear as to how much higher the free throw percentage is for one player than for another.
D.We don't know if all of the people on the team are included in the graph.
Answer: C
Step-by-step explanation:
to be a good graph the x axis and y axis need labeled
The graph could be misleading because it does not indicate if the free throws were made at home or away, it is missing the scale on the y-axis, and it doesn't specify if all team members are included.
Explanation:The statement that best describes why this graph could be misleading is A. The graph does not indicate if the free throws were made at home or away. The graph may show higher or lower percentages for certain players based on the location of the game. For example, a player may have a higher free throw percentage when playing at home compared to playing away.
Additionally, statement C is also correct. The graph is missing the scale on the y-axis, which makes it unclear how much higher or lower the free throw percentages are for each player.
Lastly, statement D is another reason why the graph could be misleading. Without knowing if all the people on the team are included, the graph may not provide an accurate representation of the overall free throw percentages of the team.
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What is the slope for 4y-2x=8
Answer:
1/2
Step-by-step explanation:
The answer would be x-2y= -4 I hope this helped!
Which polygon is irregular?
Answer:
The irregular polygon is D.
Step-by-step explanation:
An irregular polygon is a shape that doesn't have all congruent sides.
Answer:
D
Step-by-step explanation:
What is the answer to 20g + 24h?
Answer: 64g
Step-by-step explanation: added 20 by 20 and then add the 4.
Answer:it stays the same
Step-by-step explanation: because if it different letters it can’t combine
Hugo took these steps to solve the system of equations.
2 x minus 3 y = negative 11. 3 x + 2 y = negative 5.
Step 1 4 x minus 6 y = negative 11. 9 x + 6 y = negative 15.
Step 2 13 x = negative 26
Step 3 x = negative 2
Step 4 3 (negative 2) + 2 y = negative 5. Negative 6 + 2 y = negative 5. 2 y = 1. y = one-half.
Step 5 The solution is (Negative 2, one-half).
Is Hugo’s solution to the system of equations correct? Explain why or why not.
Yes, Hugo’s solution is correct.
No, Hugo should have gotten positive 2 in step three.
No, Hugo forgot to multiply both sides of the first equation in step one.
No, Hugo should have subtracted the equations instead of adding them in step 2.
Answer:
C
Step-by-step explanation:
Answer: C ) No, Hugo forgot to multiply both sides of the first equation in step one.
Step-by-step explanation:
Select all true statements.
Answer:
A) Sin A + Sin B = 1.2 Sin C
D) Sin C = 2.5 Sin A = 1.25 Sin B
E) Sin A + Sin C = 1.75 B
Step-by-step explanation:
Here, in the given triangle ABC
Base AC = 16 units, AB = 2 units, and BC = 8 units
Now, by Trigonometric Functions:
[tex]\frac{Sin A}{8} = \frac{Sin B}{16} =\frac{Sin C}{20}[/tex]
Comparing first two terms, we get:
[tex]\frac{Sin A}{8} = \frac{Sin B}{16} \\\implies 2Sin A = Sin B[/tex] ........... (1)
Also,
[tex]\frac{Sin B}{16} = \frac{Sin C}{20} \\\implies Sin C = 1.25 Sin B[/tex] ....... (2)
Comparing first and last terms, we get:
[tex]\frac{Sin C}{20} = \frac{Sin A}{8} \\\implies SinC = 2.5 Sin A[/tex] .......... (D)
Also, Sin A = 0.5 Sin B
So, the given statement Sin A = 2 Sin B is FALSE
⇒ 2.5 Sin A = 1.25 Sin B .......... (D)
Also, Sin B = 2 Sin A
⇒ Sin A + Sin B = Sin A + 2 Sin A = 3 Sin A
Also, Sin A = 0.4 Sin C
⇒3 Sin A = 3 x (0.4) Sin C = 1.2 Sin C ..
⇒Sin A + Sin B = 1.2 Sin C ........ (A)
B) Sin A - Sin B = 0.4 Sin C - 2 Sin A = 0.4 Sin C - 2 (0.4 Sin C)
= 0.4 Sin C - 0.8 Sin C = -0.4 Sin C
⇒Sin A - Sin B = -0.4 Sin C ........ (B)
So, the given statement is FALSE
E) Sin A + Sin C = 0.5 Sin B + 1.25 B = 1.75 B
⇒ Sin A + Sin C = 1.75 B ....(E)
From 2003 onward, the number of daily visitors to a website increased by 200% every two years. So, for example, the number of visitors in 2011 was 200% more than the number of visitors in 2009.
In what year was the number of daily visitors $800\%$ more than the number of daily visitors in 2003?
It takes 4 years for number of daily visitors to be 800% more than the number of daily visitors in 2003
Solution:
Let the number of visitors in 2003 be 100
From 2003 onward, the number of daily visitors to a website increased by 200% every two years
Therefore, Number of visitors in 2005 is given as:
Visitors in 2005 = 100 + 200 % of 100
[tex]Visitors\ in\ 2005 = 100 + \frac{200}{100} \times 100\\[/tex]
Visitors in 2005 is 300
Similarly, in 2007, the number of visitors is given as:
Visitors in 2007 = 300 + 200 % of 300
Visitors in 2007 = 300 + 600
Visitors in 2007 = 900
Now find the percentgae increase from 2003 to 2007
[tex]\text { Percentage increase }=\frac{\text {visitors in } 2007-\text {visitors in } 2003}{\text {visitors in } 2003} \times 100[/tex]
[tex]\text{percentgae increase} = \frac{900 - 100}{100} \times 100\\\\\text{percentgae increase} = 800[/tex]
Thus it is a 800 % increase
Number of years = 2007 - 2003 = 4 years
Thus it takes 4 years for number of daily visitors to be 800% more than the number of daily visitors in 2003
If a number increases by $200\%$, then this means that $2$ times the number is added to the original number. The result is $3$ times the original number. So, the information given in the problem means that the number of daily visitors to the website tripled every two years.
For the number of daily visitors to increase by $800\%$, it must become $9$ times its original value (that's $8$ times the original number added onto the original number). This is equivalent to tripling and then tripling again.
Relative to its value in $2003$, the number of daily visitors to the website tripled by $2005$, then tripled again by $2007$. So, $\boxed{2007}$ is the year in which this number reached $800\%$ more than its value in $2003$.
Can you Solve 4x = -60
Answer:
X = -15
Step-by-step explanation:
Divide -60 by 4
How do I simplify (5i) square
Answer:
see attached picture please
There are 3,200 students at our school. If 52% of them are boys, then how many boys are enrolled at our school?
Answer:
1664 boys
Step-by-step explanation:
3200×0.52=1664 boys
Answer:
1664
Step-by-step explanation:
Multiply 3200 by the 52% as a decimal, which is 0.52, and 3200 times 0.52 gives you the answer 1664.
To determine the best fit undergraduate program, a high school senior researches the majors offered at the universities he is considering for admissions. The internet search reports that Arizona State University lists nine of their most popular majors and the percent of student population enrolled in the programs.
_______________________________________________
Popular Majors Percent of Student Body
Biology 8%
Business Marketing 20%
Communications/Journalism 6%
Education 5%
Engineering 7%
Interdisciplinary Studies 6%
Psychology 6%
Social Sciences 10%
Visual and Performing Arts 8%
----------------------------------------------------------
The university’s enrollment is expected to reach at least 20,000 students for the fall semester.
The minimum number of students who are expected to be working towards a Social Sciences degree is
The university requires that any student who is studying Visual and Performing Arts or Communications/Journalism must perform in one of the student productions before graduation. At least 20,000 students will be performing in the university’s student productions before graduation.
In the fall semester, % of the student population will be enrolled in a degree program not listed as one of the university’s most popular.
The most popular degree offered at Arizona State University is
For the fall semester, the university should expect that students will enroll in one of the two most popular
At least 2,000 students are expected to pursue a Social Sciences degree at Arizona State University. The most popular degree is Business Marketing, and about 6,000 students are estimated to enroll in the top two most popular programs (Business Marketing and Social Sciences) in the fall semester.
Explanation:Based on the information provided about
Arizona State University's
most popular majors and their respective percentages, you can determine the minimum number of students expected to be working towards a Social Sciences degree. The
Social Sciences
program makes up 10% of the student body. Therefore, if the enrollment is expected to reach at least 20,000 students, you can expect that at least 2,000 students (10% of 20,000) will be working towards a
Social Sciences
degree. As for the most popular degree, Business Marketing is listed as comprising 20% of the student body, making it the most popular degree. The two most popular programs, Business Marketing and Social Sciences, make up 30% of the student body. So the university might expect that at least 6,000 students (30% of 20,000) will enroll in one of the two most popular programs in the fall semester.
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how do i find the mid point in A(-3,13) B(15,7) and C(-3,11)
Answer:
Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)
Step-by-step explanation:
Given that the points are A(-3,13), B(15,7) and C(-3,11)
To find the mid points :
To find midpoint of AB
Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points A(-3,13),B(15,7) respectively
Midpoint of AB[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{-3+15}{2},\frac{13+7}{2})[/tex]
[tex]=(\frac{12}{2},\frac{20}{2})[/tex]
[tex]=(6,10)[/tex]
Midpoint of AB=(6,10)
To find midpoint of BC
Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points B(15,7),C(-3,11) respectively
Midpoint of BC[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{15-3}{2},\frac{7+11}{2})[/tex]
[tex]=(\frac{12}{2},\frac{18}{2})[/tex]
[tex]=(6,9)[/tex]
Midpoint of BC=(6,9)
To find midpoint of CA
Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points C(-3,11),A(-3,13),respectively
Midpoint of CA[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{-3-3}{2},\frac{11+13}{2})[/tex]
[tex]=(\frac{-6}{2},\frac{24}{2})[/tex]
[tex]=(-3,12)[/tex]
Midpoint of CA=(-3,12)
Therefore Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)
7x + 2y = -1
3x – 4y = 19
Answer: Y = - 4 & x = 1
Step-by-step explanation:
Systems of linear equations: We will solve this using substitution but you can use 2 more ways.
7x + 2y = -1
2x - 4y = 19
Leave X alone first: -------------------
10x - 2y = 18
10x/10 = 18 + 2y/10
x = 9/5 + y/5
Solve for y:
7(9/5 + y/5) + 2y = -1
63/5 + 7y/5 + 2y - 1
63/5 + 7y/5 = 10y/5 = -1
63/5 + 17y/5 = -1 (-5/5)
17y/5 = -68/5 (cancel the 5)
y = -68/17
y = - 4 (Your Answer)
7x + 2(- 4) = -1
7x + (-8) = -1
7x = 7
x = 1
CHECK=
7(1) + 2(-4) = -1
7+ (-8) = -1.
-1=-1
Answer:
(1, -4).
(x = 1, y = -4).
Step-by-step explanation:
7x + 2y = -1
3x – 4y = 19 Multiply the first equation by 2:
14x + 4y = -2 Adding:
17x = 17
x = 1.
Plug this into the second equation:
3(1) - 4y = 19
-4y = 19 - 3 = 16
y = -4.
Help me on my midterm.!
Last Option: "The division property is used to create step 4" is the correct answer
Step-by-step explanation:
Given equation is:
[tex]6(3x-4)-26 = 40[/tex]
Step 1: Distributive property
[tex]18x-24-26 = 40\\[/tex]
Step 2: Simplifying
[tex]18x-50 = 40[/tex]
Step 3: Addition Property of Equality
[tex]18x-50+50 = 40+50\\18x = 90[/tex]
Step 4: Division Property of Equality
[tex]\frac{18x}{18} = \frac{90}{18}\\x = 5[/tex]
Hence,
Last Option: "The division property is used to create step 4" is the correct answer
Keywords: Linear equation, variables
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Find the x and y intercepts of -2x - 4y = -12
Answer: x-intercept(6,0) & y-intercept(0,3)
Step-by-step explanation: To find the x-intercept, subsitutue zero in for y and solve for x, and vice versa to solve for y.
----------------------
Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!
- Cutiepatutie ☺❀❤
What is the solution to –2(8x – 4) < 2x + 5?
x > x is greater than StartFraction 1 Over 6 EndFraction.
x < x is less than StartFraction 1 Over 6 EndFraction.
x > 6
x < 6
Answer:
x is greater than StartFraction 1 Over 6 EndFraction.
Step-by-step explanation:
–2(8x – 4) < 2x + 5
⇌ –16x + 8 < 2x + 5
⇌ 3 < 18x
⇌ 1/6 < x
⇌ x > 1/6
Answer:
A
Step-by-step explanation:
help please 10 points !!images below
Answer for Question 1 is option 2
Answer for Question 2 is option 3
Answer for Question 3 is option 3
Step-by-step explanation:
For question 1 by plotting the two points we get the coordinates as (-2, 3) and (2, 1) where the x values are -2, 2 and the y values are 3, 1 respectively. By substituting values of x in the formula given we get that equation 2 satisfies the values of y as in the graph.
For question 2 the plotted line is split into two parts where one half is for values of x <2 and the other half is for values of x>2. By finding out the coordinates we get them as (2,-2), (1,-2.5) and (0,-3) for x<2 and by substituting the values of x in the formula we get option 3 as our answer.
For question 3 we need to find the value of y when x=3 and the first condition is only for values greater than 3 so we take the second condition and substitute the value of x=3 and we get the value of y as 5 so the answer is option 3
What is 980 divided by 41
Answer:
23.902
Step-by-step explanation:
x² - 6x – 40=0
Complete the square
Answer:
Step-by-step explanation:
x^2 - 6x - 40 = 0.....get the -40 to the other side
x^2 - 6x = 40....now take half of ur x term (6)....so its 3...then square it (3^2 = 9)...now add 9 to both sides
x^2 - 6x + 9 = 40 + 9
(x - 3)(x - 3) = 49
(x - 3)^2 = 49...take sqrt of both sides, eliminating the ^2
x - 3 = sqrt 49
x = 3 (+ - ) 7
x = 3 + 7 = 10 or x = 3 - 7 = -4
so x = 10 or x = -4
What is the value of the expression when y = 2?
3(y + 2)
Answer:
12
Step-by-step explanation:
3[y+2]
2+2= 4
3 multiplied by 4 is 12
Answer: 12
Step-by-step explanation: Since y = +2, we simply plug a +2 in for y in the expression. So we have 3(2 + 2).
Following your order of operations, you should simplify what's inside the parentheses first so 2 + 2 simplifies to 4.
Bring down your 3 and you have 3(4) which equals 12.
The ratio of boys to girls is 7:12. If there are 76 children how many are girls?
Answer:
Step-by-step explanation:
I need help
Answer:
28 girls
Step-by-step explanation:
Given girls : boys ===> 7 : 12
i.e.
fraction all children who are girls = 7 / (7 + 12) = 7 / 19
fraction all children who are boys = 12 / (7 + 12) = 12 / 19
given that there are 76 children
number of girls = fraction of all children who are girls x total number of children
= 7/19 x 76
= 28 girls
On a boat, a cabin's window is in the shape of an isosceles trapezoid, as shown below. What is the area of the window?
ANSWER: 182 inches
STEP-BY-STEP EXPLANATION:
Since, it is an isosceles trapezoid, then area of an isosceles triangle is given by: [tex]\frac{1 (a+b)}{2}[/tex] × h
where a and b are the two parallel sides of the triangle and h is the height of an isosceles triangle.
Now, a= 12 inches and b= 2+2+12=16 inches and h=13 inches.
[tex]\frac{1 (12+16)}{2}[/tex] × 13 = 182 inches
an airplane lands at an airport 80 miles west and 30 miles north of where it took off. How far apart are the airports.
Answer:
85.44 miles apart
Step-by-step explanation:
According to the question;
The airplane flew 80 miles west and 30 miles northWe are supposed to determine how far apart are the airports.
The shortest distance will be the displacement from the initial point.We are going to use the Pythagoras theorem;a² + b² = c² , where a and b are the legs of a right angled triangle and c is the hypotenuse.Therefore, in this case; our legs will be 30 miles and 80 miles, so we need to determine the hypotenuse;That is;
c² = 80² + 30²
= 6400 + 900
= 7300
c = √7300
= 85.44
Thus, the airports are 85.44 miles apart
Approximately how many ounces are equivalent to 1 kilogram?
Answer: 35.27 oz
The answer is: The change of 1 kg ( kilogram ) unit for a weight and mass measure equals = into 35.27 oz ( ounce ) as per its equivalent weight and mass unit type measure often used.
Approximately, 1 kilogram is equivalent to 35.3 ounces. This calculation is achieved by starting with the knowledge that 1 kilogram is 1000 grams, then converting this measurement to ounces knowing that 1 gram equals 0.0353 ounces.
Explanation:The topic at hand is the conversion between weight metrics, specifically how many ounces are approximately equivalent to a kilogram. It's important to note that 1 kilogram is approximately equivalent to 35.274 ounces. Here's why:
We understand from the given information that 1 ounce is produced by a mass of 28.35 grams (abbreviated as g). Given that 1 kilogram (kg) is equal to 1000 grams, to find the equivalent of a kilogram in ounces, we need to convert 1000 grams to ounces:
Step-by-Step Calculation
Start with 1 kilogram, which is equivalent to 1000 grams.Knowing that 1g equals to 0.0353 ounces, multiply 1000 grams by 0.0353 oz/g. This gives us 35.3 ounces.So, 1 kilogram is approximately equivalent to 35.3 ounces.
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- the line through (3, 7) and (-1, 4) --
Answer:
[tex]y = \frac{3}{4}x + \frac{19}{4}[/tex]
Step-by-step explanation:
We have to get the equation of the straight line through the points (3,7) and (-1,4).
Now, we know that the two-point formula of a straight line passing through the two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by
[tex]\frac{y - y_{1} }{y_{1} - y_{2}} = \frac{x - x_{1} }{x_{1} - x_{2}}[/tex].
So, in our case, the equation of the straight line will be
[tex]\frac{y - 7}{7 - 4} = \frac{x - 3}{3 + 1}[/tex]
⇒ 4(y - 7) = 3(x - 3)
⇒ 4y - 28 = 3x - 9
⇒ 4y = 3x + 19
⇒ [tex]y = \frac{3}{4}x + \frac{19}{4}[/tex] (Answer)
GIVING BRAINLIEST NEED HELP PLZ!!!!
Simplify ( x - 2) - (6 x - 9)
Answer:
Subtracting polynomials is simply subtracting the like terms
(x-2)-(6x-9)
First you want to subtract your x from 6x
x-6x= -5x
Than you would subtract -2 and -9
-2- -9=7
-2+9=7
Your final answer would be
-5x+7
Hope this helps ;)
Step-by-step explanation:
What is the product? (x + 3)(2 x minus 1)
Answer:
Your final answer will be 2x^2 + 5x -3
Step-by-step explanation: