Example 2. Simple interest on $5000 over 4 years is $1800, what is the interest rate? Example 3. If you borrow $1200 at a 5% annual interest rate, how long will it take for the total amount owed to reach $1300? Example 4. Find the principal if the simple interest in 14 days at 25% per annum is 100.
I need help with all 4 questions plz
Find a polynomial equation that has roots of -2 and double root 3
Answer:
x³ + 2x² -3x +6
Step-by-step explanation:
We need to find the polynomial whose roots are ,
-2 , √3 and √3.Say of we have zeroes as , α , β and γ , then the polynomial is ,
=> p(x) = k[ (x - α ) ( x - β) ( x - γ) ]
where k is constant. Substituting the respective values , we have ,=> p(x) = k [ ( x - (-2)) ( x - √3) ( x -√3)]
=> p(x) = k[ (x+2)(x² - 3)]
=> p(x) = k[ x(x² - 3) + 2(x² - 3) ]
=> p(x) = k[ x³ - 3x + 2x² - 6 ]
=> p(x) = k[ x³ + 2x² - 3x - 6 ]
Hence the cubic polynomial is x³ + 2x² - 3x + 6 .It’s my final and I haven’t paid attention
Answer:
f(x)= (1/2)x-3
Step-by-step explanation:
Bert measured a swimming pool and made a scale drawing. The scale of the drawing was
1 centimeter = 1 meter. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Submit
Use the Law of Cosines to find the measure of ∠A. Round to the nearest degree.
a = 12, b = 5, c = 9
Use: a² = b² + c² – 2bc cos A
Answer:
Solution given:
a = 12, b = 5, c = 9
We have
: a² = b² + c² – 2bc cos A
12²=5²+9²-2×5×9 cos A
12²-25-81=-90 cos A
cos A=38/-90
A=cos -1(-19/45)
A=115°
is a required answer.
The following two-way table describes student's
after school activities. Find the probability that a
randomly selected student works, given that it's a
senior.
Grade
Sports
Music/Drama
Work
Sophomore
20
7
3
Junior
20
13
2
Senior
25
5
5
P( Work | Senior) = [?]
Round to the nearest hundredth.
Answer:
[tex]P(Work | Senior) = 0.14[/tex]
Step-by-step explanation:
Given
The attached table
Required
[tex]P(Work | Senior)[/tex]
This is calculated using:
[tex]P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}[/tex]
This gives:
[tex]P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}[/tex]
From the table:
[tex]n(Work \ n\ Senior) = 5[/tex]
[tex]n(Senior) = 25 + 5+ 5 = 35[/tex]
So:
[tex]P(Work | Senior) = \frac{5}{35}[/tex]
[tex]P(Work | Senior) = 0.14[/tex]
Answer:
14%
Step-by-step explanation:
add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).
Three years ago the sum of the ages of father and his son was
48 years and three years hence father's age will be three times
that of his son. Find the present ages of the father and his son.
Answer:
The father is 42 years old and the son is 12 years old.
Step-by-step explanation:
Since three years ago the sum of the ages of father and his son was 48 years, and three years hence father's age will be three times that of his are his, to find the present ages of the father and his are his, the following calculations must be performed:
F + S = 48
F + 6 + S + 6 = 3S
34 + 14 = 48 /// 34 + 6 = 40 --- 14 + 6 = 20 (x 3 = 60)
38 + 10 = 48 /// 38 + 6 = 44 --- 10 + 6 = 16 (x 3 = 48)
40 + 8 = 48 /// 40 + 6 = 46 --- 8 + 6 = 14 (x 3 = 42)
39 + 9 = 48 /// 39 + 6 = 45 --- 9 + 6 = 15 (x 3 = 45)
39 + 3 = 42
9 + 3 = 12
Therefore, the father is 42 years old and the son is 12 years old.
Help just help please. !!!
Answer: The maximum value is -3.75
Note: -3.75 = -15/4
=============================================================
Explanation:
The given quadratic is in the form y = ax^2 + bx + c, where,
a = -1b = 1c = -4We'll plug the values of 'a' and b into the formula below
h = -b/(2a)
h = -1/(2(-1))
h = 1/2
h = 0.5
This represents the x coordinate of the vertex. Recall the vertex is (h,k).
Plug this x value into the function to find its corresponding y coordinate
y = -x^2 + x - 4
y = -(0.5)^2 + 0.5 - 4
y = -3.75
The vertex is located at (0.5, -3.75)
Since a < 0, this means the parabola opens downward and that the vertex is the highest point on the parabola. Therefore, the largest y can get is y = -3.75 which we consider the maximum.
The graph visually helps confirm this (see image attachment).
Side note: -3.75 = -15/4
-------------------
Here's another way we can find the vertex (h,k). We'll complete the square to get the function into vertex form
y = -x^2 + x - 4
y + 4 = -x^2 + x
y + 4 = -(x^2 - x)
y + 4 = -(x^2 - x + 0)
y + 4 = -(x^2 - x + 0.25 - 0.25) .... see note below
y + 4 = -(x^2 - x + 0.25) -(-0.25)
y + 4 = -(x^2 - x + 0.25) + 0.25
y + 4 = -(x - 0.5)^2 + 0.25
y = -(x - 0.5)^2 + 0.25 - 4
y = -(x - 0.5)^2 - 3.75
This is in the form y = a(x-h)^2 + k where (h,k) = (0.5, -3.75).
Note: The x coefficient is -1 which cuts in half to -0.5, then that squares to 0.25
HELP ME PLEASEEEEEEEEEEEEEEEEEEE
Answer:
the last one
Step-by-step explanation:
Answer:
The 2nd one (the one you chose) is right thats the answer
Step-by-step explanation:
Work out cube root of 512 : reciprocal of 0.4. Give your answer in the form n : 1
Step-by-step explanation:
Thanks, so cube root of 512 is 8 and reciprocal of 0.4 is 2.5 then:
8 : 2.5 / divide both by 2.5 to get:
3.2 : 1 that's my answer right?
The correct form of the ratio of cube root of 512: reciprocal of 0.4 is 3.2:1
What is a cube root?
It is a number y such that y to the power 3 is equal to x.
How to find ratio?
We have to find the ratio of cube root of 512 and the reciprocal of 0.4 which will be as follows
cube root of 512: reciprocal of 0.4
8: 1/0.4
8=2.5
dividing by 2.5
3.2 : 1
Hence the ratio will be 3.2 :1 of cube root of 512 and the reciprocal of 0.4
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Help please
(Worth 10 points)
Please respond with a actual answer
*No robots no bad links*
Five friends are sharing 4 fruit bars. Each friend gets the same amount.
How much fruit bar does each friend get?
Answer:
4/5 of a fruit bar
Step-by-step explanation:
Daniel measures the growth of his tomato plant and records the results in the table.
What was the average rate of growth during this time period for his plant to thenearest tenth?
Answer:
1.2
Step-by-step explanation: it just is
A vector is used to express a car's change in position, or displacement, by tracking its motion over a large area defined by a coordinate grid. If the car begins at (−3,−5) and ends at (5,9), which of these expresses the car's displacement in vector form?
A
(14,8)
B
(10,12)
C
(8,14)
D
(2,4)
Answer:
The correct answer is option C: (8, 14).
Step-by-step explanation:
The car's displacement in vector form can be found by subtracting the initial points from the final points.
Initial: (x₁, y₁) = (-3, -5)
Final: (x₂, y₂) = (5, 9)
For the x-coordinate, we have:
[tex] d_{x} = x_{2} - x_{1} = 5 - (-3) = 8 [/tex]
And for the y-coordinate, we have:
[tex] d_{y} = y_{2} - y_{1} = 9 - (-5) = 14 [/tex]
The car's displacement in vector form is:
[tex] d = (d_{x}, d_{y}) = (8, 14) [/tex]
Therefore, the correct answer is option C: (8, 14).
I hope it helps you!
Could you please explain in detail how to graph this. Thank you:)
I need help, please !
Answer: the answer is 8 because
Step-by-step explanation:
please help the will get a brilliantaal
Two friends decided to open up bank accounts. Israel deposited $1000 into an account with a growth rate of 15%, and Dameon deposited $3,000 into an account with a growth rate of 2%. After 10 years, who will have more money in their account?
Answer:
Isreal
Step-by-step explanation:
15% of 1000 is 150x10=1500
2% of 3000 is 60x10=600
Can someone please help me? If you cannot think of anwer, leave me alone aight?
I need somebody to explain why the surface area of the cylinder in the image is
351.86 square inches. Yes, i know the answer but still clueless how to solve for that. (There was a test and I got the answer wrong then it revealed the right answer)
Will mark brainliest if someone truly helps me.
Answer:
Formula for to find out the surface area of a cylinder = 2πrh+2πr^2
As the radius of the cylinder (4/2) cm = 2cm
Then the surface area of the cylinder
= 2πrh + 2πr^2
=( 2×22/7×2×6 + 2×22/7 × 2^2) cm^2
= (528/7 + 176/7) cm^2
= 704/7 cm^2
=100.571428571 cm^2
=15.58860260571021 in^2 (ans)
This the answer
Trying to finish this test at 3:30 am plz help
Given:
The given sum is:
[tex]\sum _{k=4}^9(5k+3)[/tex]
To find:
The expanded form and find the sum.
Solution:
We have,
[tex]\sum _{k=4}^9(5k+3)[/tex]
The expanded form of given sum is:
[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]
[tex]\sum _{k=4}^9(5k+3)=213[/tex]
Therefore, the correct option is C.
The area of the outer rectangle above is 80 ft, and the area of the inner rectangle is 68 ft. What is the area of the shaded region?
Answer:
B
Step-by-step explanation:
is the right answer
The area of the shaded region is 12 feet². The correct option is A.
What is a rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that the area of the outer rectangle above is 80feet². The area of the inner rectangle is 68feet². The area of the shaded region=area of the outer rectangle- the area of the inner rectangle.
The area of the shaded region=(80-68 )feet²
The area of the shaded region= 12feet²
Thus, the area of the shaded region is 12feet².
Learn more about rectangles here:
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Tammy has scored 82, 78, and 93 on her previous three tests. What score does she need on her next test so that her average (mean) is 81?
Answer:
She needs a grade of 71 on her next text.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
Tammy has scored 82, 78, and 93 on her previous three tests.
Thus, her grades are 82, 78, 93 and x, in which x is her grade in the fourth test.
There are 4 tests.
What score does she need on her next test so that her average (mean) is 81?
We have to find x when the mean is 81. So
[tex]\frac{82 + 78 + 93 + x}{4} = 81[/tex]
[tex]253 + x = 324[/tex]
[tex]x = 324 - 253[/tex]
[tex]x = 71[/tex]
She needs a grade of 71 on her next text.
Chile I’m struggling
Answer:
the answer is c
Step-by-step explanation:
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1070 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number. SAT score =
(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =
(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =
Answer:
a) SAT score = 1075
b) ACT score = 19.2.
c) ACT score = 27.9.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score
SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]
51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 1070}{204}[/tex]
[tex]X - 1070 = 0.025*204[/tex]
[tex]X = 1075[/tex]
SAT score = 1075.
(B) What would be the equivalent ACT score for this student?
ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 0.025*5.2[/tex]
[tex]X = 19.2[/tex]
ACT score = 19.2.
(C) If a student gets an SAT score of 1417, find the equivalent ACT score.
Z-score for the SAT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1417 - 1070}{204}[/tex]
[tex]Z = 1.7[/tex]
Equivalent score on the ACT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 1.7*5.2[/tex]
[tex]X = 27.9[/tex]
ACT score = 27.9.
A section of a deck is shaped like a trapezoid. For this section, the length of one base is 41 feet, and the length of the other base is 36 feet. The height is 20 feet. What is the area of this section of the deck?
Answer:
Step-by-step explanation:
Please help me solve this problem
Answer:
90°
Step-by-step explanation:
It's simple, the angle of a line is 180°
∠EFG=90°
Line GD-∠EFG=180°-90°=90°
Please mark brainliest!
What is the speed if the distance is 234 MI and time is 3 hrs
Answer:
speed = 78 miles per hour
Step-by-step explanation:
Speed is distance divided by time
speed = 234 miles / 3 hours
speed = 78 miles per hour
Practice
what is sin(-30*) ? Sketch a graph to help determine the answer.
a. 0.5
b. -0.5
c. 1
d. 0
Please select the best answer from the choices provided
Answer:
B. -0.5
Step-by-step explanation:
I calculated it logically
To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades: 3.5 in a 5 credit Math course 2.2 in a 2 credit Music course 2.5 in a 5 credit Chemistry course 3.2 in a 4 credit Journalism course What is the student's GPA for that term
Answer: 2.95
Step-by-step explanation:
The students GPA for the term will be calculated as the weighted score divided by the number of units. This will be:
= (3.5 × 5) + (2.2 × 2) + (2.5 × 5) + (3.2 × 4) / (5 + 2 + 5 + 4)
= (17.5 + 4.4 + 12.5 + 12.8) / 16
= 47.2 / 16
= 2.95
Therefore, the GPA is 2.95
will give brainliest
Answer:
Step-by-step explanation:
1/48 + 5/6
The LCD of 48 and 6 is 48 so we have:
1/48 + 40/48
= 41/38
Answer:
41/48
Step-by-step explanation:
Original price: $130
Discount: 60%
Sale price:?
Answer:
$52
Step-by-step explanation:
first you find out what 60% of 130. all you need to do is put a decimal before the percent and multiply it with the cost, in this case 0.6 x 130, which results in 78. next you subtract the percentage result from the total cost to get your answer of $52.