Answer:
60
Step-by-step explanation:
number of miles driven north plus 34 equal 94.
subtract 94 from 34 to get your answer.
Mrs. Lopez drives 60 miles north.
The completed number sentences are:
60 + 34 = 94 and 94 - 34 = 60.
What is number sentence?Let's assume Mrs. Lopez drives x miles north.
The number sentence for the total distance she drives can be written as:
x + 34 = 94
This equation represents the sum of the distance she drives north (x) and the distance she drives west (34), which equals the total distance she drives (94).
To find the value of x, subtract 34 from both sides of the equation:
x = 94 - 34
Simplifying the expression, we have:
x = 60
Therefore, Mrs. Lopez drives 60 miles north.
The completed number sentences are:
60 + 34 = 94 and 94 - 34 = 60.
Read on number sentences on https://brainly.com/question/28839703
#SPJ3
NEED HELP URGENTLY!!!!
The population of the United States in 2005 was approximately 295,500,000 and the land area was 3,806,000 square miles. The population increased by 5.1% in 2015. To the nearest whole number, how much did the population density, in people per square mile, increase from 2005 to 2015?
3
4
5
6
Answer:
4 people per square mile
Step-by-step explanation:
----Population density = number of people divided by land area.
Back I 2005,the population density of the US was: 295500000/3806000= 77.6 people per square miles.
----If the population increased by 5.1%,the new population of residents in the US will be
100% + 5.1% = 105.1%
105.1/100 × 295500000
= 310,570,500.
--- The new population density of the US in 2015 will be
310,570,500 ÷ 3,806,000
= 81.6 persons per square mile
---- To find out the difference in population from 2005 to 2015,we have to do nothing else but subtract the Population Density (PD) of 2015 from 2005
81.6 - 77.6 = 4 persons per square mile
:) How
any nore novies does Student B have than Student A?
Sudent A OOOO
Sudent B 0000000
2 more
8 times as many
4 more
4 times as many
Answer:
student b has 4 more movies
Step-by-step explanation:
Answer:
4 more
Step-by-step explanation:
Which equation represents the area of one base of a cylinder if the radius is doubled?
A. B= = more
B. B = 3.72
C. B = 27012
D. B = 4772
Please select the best answer from the choices provided
о А
Answer:
[tex]B_2=4\pi r^2[/tex]
Step-by-step explanation:
we know that
The area of the base of a cylinder is given by the formula
[tex]B=\pi r^{2}[/tex]
where
r is the radius of the circular base
If the radius is doubled
then
[tex]r=2r[/tex]
The new base area is
[tex]B_2=\pi (2r)^{2}\\B_2=4\pi r^2[/tex]
so
[tex]B_2=4B[/tex]
therefore
The new area of the base is 4 times the area of the original base
Vijay has a collection of 50 number cubes that are each 1 cubic inch. He finds a box that is 2 inches high. He fits 10 cubes into the bottom of the box. Can Vijay fit all his number cubes into the box? How many can he fit in?
Answer:
Vijay cannot fit all the cubes into the box, he can only fit 20 cubes into the box
10 x 2 = 20 cubes
He would need 5 boxes to fit all the cubes
Hope this helps <3
A cone frustum is inscribed in a sphere of radius 13. If one of the bases of the frustum is a great circle of the sphere, and the other base has radius 12, what is:
The height of the frustum?
Answer:
5
Step-by-step explanation:
According to the question, A cone frustum is inscribed in a sphere of radius 13. If one of the bases of the frustum is a great circle of the sphere, and the other base has radius 12.We are now asked to find the height of the frustum.
---The height of this frustum is equal to the distance of its smaller base from the center of the sphere.
Therefore,it is assigned the pattern
H = √(r1² - r2²
Where r1 is the radius of the sphere
And r2 is the radius of the other base of the frustum
H is the height that we are looking for
H = √(13² - 12²)
= √( 169 - 144 )
= √ 25
H = 5
Final answer:
The height of the frustum inscribed in a sphere with a radius of 13 and one base having a radius of 12 is found to be 10 units using the Pythagorean theorem.
Explanation:
To find the height of the frustum inscribed in a sphere of radius 13, where one base is a great circle of the sphere, and the other base has radius 12, we can use geometry and Pythagorean theorem.
Consider the right triangle formed by the radius of the sphere, half of the frustum height (since the center of the sphere is midway of the frustum's height for the configuration given), and the radius of the smaller base of the frustum.
The radius of the sphere is 13, and the radius of the smaller base is 12.
Using the Pythagorean theorem (a² + b² = c²), we can find the half-height of the frustum.
So, we have:
122 + b² = 132
144 + b² = 169
b² = 25 => b = 5
Thus, the full height (h) of the frustum is 10 units.
Line segment MN is shown below. If point P(x,y) partitions the line segment
into the ratio MP:PN = 1:2 then determine the values of x and y.
Line segment:
Point M: (-6,2).
Point N: (9. – 4)
Answer:
P (-1 , 0)
Step-by-step explanation:
M (-6 , 2) N (9 , -4) P (x , y)
horizontal distance of M and N = 9 - (-6) = 15
vertical distance of M and N = 2 - (-4) = 6
1/3 from x coordinate of M (-6): -6 + 15/3 = -1 This is x coordinate of point P
1/3 from y coordinate of M (2): 2 - 6/3 = 0 This is y coordinate of point P
P (x , y) i.e P (-1 , 0)
check: distance of MP = √(-1 - (-6))² + (0 - 2)² = √29 = 5.385
distance of PN = √(-1 - 9)² + (0 - (-4))² = √116 = 10.77
MP / PN = 5.385 / 10.77 = 0.5 = 1/2
The values of x and y that partition the line segment MN into the ratio 1:2 are x = 3 and y = -4.
Explanation:To determine the values of x and y that partition the line segment MN into the ratio MP:PN = 1:2, we can use the section formula. The section formula states that the coordinates of a point P(x,y) that partitions a line segment with endpoints M(x1, y1) and N(x2, y2) into the ratio m: n are given by:
x = (nx1 + mx2) / (m + n)
y = (ny1 + my2) / (m + n)
In this case, M(-6, 2) and N(9, -4), and the ratio is 1:2. Plugging these values into the section formula, we get:
x = (2*9 + 1*(-6)) / (1 + 2) = 3
y = (-4*2 + 2*(-4)) / (1 + 2) = -4
Therefore, the values of x and y that partition the line segment MN are x = 3 and y = -4.
Learn more about Determine values of x and y for a partitioned line segment here:https://brainly.com/question/33722858
#SPJ11
(Algebra Word Problems) Janice, Rene, and Lucinda shared a summer
babysitting job. Janice babysat twice as many hours as Rene. Lucinda
babysat 10 more hours than Janice. If r represents the number of hours
that Rene babysat, which expression represents the number of hours that
Lucinda babysat? *
R+10
2r + 10
2(r + 10)
10 x 20
Answer:
r2+A
Step-by-step explanation:
lalalalalalalalalalalalala
LOOK AT THIS ASAP, it's EASY! GIVING YOU 15 to solve an easy math question. Just order these from the least amount of players to the greatest. PLZ HELP.
Answer:
Bulldogs
Cardinals
Tornado
Step-by-step explanation:
Cardinals: 31 injuries
Tornado: 31 injuries
Bulldogs : 17 injuries
I think I did this right and i counted them twice, but they are the same so it doesn't matter where you put them and if this is wrong then im sorry but i counted them several times. If this is right can I get a brainliest?
the equation y=-7x-5 and another equation have a solution of (-2,9). what is the second equation?
I'm guessing there's a menu of choices to go with this one, and we just need to try (-2,9) with each choice. But it's a much more interesting problem without the menu.
First we verify (-2,9) is on the line y=-7x-5,
-7(-2)-5 = 14-5 = 9, good.
There's a whole family of possibilities for the second equation, basically all the other lines through (-2,9). Believe it or not, that's called a pencil of lines. We need two parameters a and b, whose values only matter in ratio, to represent all these. If we tried to do it with just the slope we'd miss one line, the vertical line x=-2.
We'll do the line through (-2,9) and (a,b). A little thought tells us it's
(a + 2)(y - 9) = (b - 9)(x + 2)
When we plug in (-2,9) we get 0=0, good. When we plug in (a,b) we get
(a + 2)(b - 9) = (b - 9)(a + 2)
which is also true.
(a + 2)(y - 9) = (b - 9)(x + 2)
(b - 9)x - (a+2)y = -9(a + 2) - 2(b-9)
(b - 9)x - (a+2)y = -9a - 2b
We can choose any a and b and we'll get the line through (-2,9) and (a,b), so it will have a solution (-2,9) where it meets y = -7x - 5.
We need to make sure (a,b) isn't already on y = -7x - 5 which is the same line twice.
For arbitrary a,b, b ≠ -7a - 5, the lines y = -7x - 5 and
(b - 9)x - (a+2)y = -9a - 2b
meet at exactly one point, namely (-2,9)
Let's generate a few and plot. We'll do a vertical and horizontal an a couple of others.
a=-2, b=0, (b - 9)x - (a+2)y = -9a - 2b
-9x = 18
x = -2
a=0, b=9, (b - 9)x - (a+2)y = -9a - 2b
-2y = -18
y = 9
a=1, b=1, (b - 9)x - (a+2)y = -9a - 2b
-8x - 3y = -11
a=1, b=3, (b - 9)x - (a+2)y = -9a - 2b
-6x - 3y = -15
2x + y = 5
plot y=-7x+5, x = -2, y = 9, -8x - 3y = -11, 2x - y = 5
What is the equation used to find the nth term of the arithmetic sequence: -9, -4 1, 6, 11...
a^n =-9-5n
a^n =5-9 (n-1 )
a^n =−9+(n−1)⋅5
a^n=-9 (5)^(n-1)
Answer:
a^n=-9+(n-1).5
Step-by-step explanation:
Arithmetic sequence=a+(n-1)d
a=-9
n=?
d=+5
Arithmetic sequence=-9+(n-1)5
=-9+5n-5
Collect like terms
-9-5+5n
-14+5n
So the final answer is
an=-9+(n-1).5
Find the 5th term of the expansion of ( 6x + 6y)^11
The 5 th term of the given expression is 330[tex](6x)^{7}( 6y)^{4}[/tex].
Step-by-step explanation:
Given,
[tex](6x+6y)^{11}[/tex]
To find the 5th term of the given expression.
Formula
In a binomial series [tex](a+b)^{n}[/tex], the r th term is = nC(r-1) [tex]a^{n-r-1} b^{r-1}[/tex], where,
nC(r-1) = [tex]\frac{n!}{(r-1)!(n-r+1)!}[/tex]
Now,
Putting, n=11, r = r, a=6x and b=6y we get,
5 th term = 11C4[tex](6x)^{7}( 6y)^{4}[/tex]
= [tex]\frac{11!}{4!7!}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]
= [tex]\frac{11X10X9X8X7!}{7!X4X3X2X1}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]
= 330[tex](6x)^{7}( 6y)^{4}[/tex]
Here is the answer.
Find the arithmetic mean An of the given terms. A(n-1)=-8, A(n+1)=-9
[tex]a_n=\frac{a_{n-1}+a_{n+1}}{2} \\a_n=\frac{-8+(-9)}{2} =-8,5[/tex]
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
P.S. Hello from Russia :^)
Final answer:
The arithmetic mean An between A(n-1) = -8 and A(n+1) = -9 is calculated by taking the average of these two terms, resulting in An = -8.5.
Explanation:
To find the arithmetic mean An between A(n-1) and A(n+1), we use the definition of the arithmetic mean for a sequence of numbers. The mean of two numbers is simply the sum of those numbers divided by two, which can be represented by the formula: mean = (a + b) / 2. Given A(n-1) = -8 and A(n+1) = -9, we can set up the formula as follows:
An = (A(n-1) + A(n+1)) / 2
Substituting the given values results in:
An = (-8 + (-9)) / 2
An = (-17) / 2
An = -8.5
Therefore, the arithmetic mean An of the given terms is -8.5.
Isoke is solving the quadratic equation by completing the square.
10x2+40x-13=0
10x2+40x=13
A(x2+4x)=13
What is the value of A?
-13
4
10
40
Answer:
C. 10Step-by-step explanation:
10 gets carried down.
The value of A in A(x² + 4x) = 13 that gives 10x² + 40x - 13 = 0 is 10.
What is a quadratic function?A quadratic function is in the form:
y = ax² + bx + c
Given that:
10x² + 40x - 13 = 0
Solving using completing the square:
10x² + 40x = 13
10(x² + 4x) = 13
The value of A in A(x² + 4x) = 13 that gives 10x² + 40x - 13 = 0 is 10.
Find out more on quadratic function at: https://brainly.com/question/1214333
The Cold Be Gone Company conducted a study where 100 participants were assigned to either receive a cold
medicine or not receive a cold medicine. The Cold Be Gone Company then recorded whether the participant's
cold lasted 7 days or longer. The Venn diagram below shows their data.
Complete the following two-way frequency table.
Received cold medicine
Did not receive cold medicine
Cold lasted longer than 7 days
Cold did not last longer than 7 days
Cold medicine
Cold longer than 7 days
27
23
20
30
Answer: Received cold medicine Did not receive cold medicine
Cold lasted longer than 7 days 23 20
Cold did not last longer than 7 days 27 30
Step-by-step explanation:
i hope it helps
To complete the two-way frequency table, calculate the values for each cell based on the given information.
Explanation:To complete the two-way frequency table, we need to fill in the missing values. Given that there are 100 participants in total, we can calculate the value for each cell. Starting with the top left cell, which represents participants who received the cold medicine and had their cold last longer than 7 days, the value would be 27. Similarly, we can calculate the values for the other cells in the table.
Learn more about Completing a two-way frequency table here:https://brainly.com/question/17175792
#SPJ2
Collins Middle School has 266 sixth grade students. If the sixth grade is 35% of the total school, how many students are in the middle school?
Answer:
93 students
Step-by-step explanation:
Answer:
266-----------35%
x----------------100%
x=(266 * 100%) / 35%= 760
There are 760 students in the middle school
Step-by-step explanation:
We solve this problem by the rule of three.
There are 7 math folders on a classroom shelf. This is 1/3 of the total number of math folders in the classroom. what is the total of number of math folders in the classroom?
Answer: 21
Step-by-step explanation:
1/3 = 7
7 * 3 = 21
1/3 = 7/21
Answer:
21
Step-by-step explanation:
PLZZ HELP IM STUPITT SORRY AND HURRYYYY
Answer:
9.9 cm²
Step-by-step explanation:
Base = 2.6x3 which is 7.8/ 2 is 3.9.
Faces = 4x3 which is 12/2 is 6
Then, add those together to get 9.9
It’s not A can someone plz help me with this
Answer:
x = 4.92
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin 38 = x/8
Multiply each side by 8
8 sin 38 = x/8 *8
8 sin 38 = x
4.925291803 =x
Simplify.
(2x^2-5x+3) - (-x^2+4x-5)
Answer:
x^2-9x+8
Step-by-step explanation:
(2x^2-5x+3)-(-x^2+4x-5)
Open the bracket first
2x^2-5x+3+x^2-4x+5
Collect like terms
2x^2+x^2-5x-4x+3+5
x^2-9x+8
So the final answer is x^2-9x+8
Tim has two spinners , spinnerA and spinner B. Each spinner can only land on red or blue . The probability that spinner A will land on red is 0.5. The probability that spinnerB will land on red is 0.6. Tim spins spinner A once and he spins spinnerB once. He does this a number of times . The number of times both spinners land on red is 84. Workout an estimate for the no of time both spinners land on blue.
Answer:
56Step-by-step explanation:
Spinner A
Probability of red = 0.5, Probability of blue = 0.5Spinner B
Probability of red = 0.6, Probability of blue = 0.4Probability of both A and B land on red:
0.5*0.6= 0.3Number of attempts to get outcome of 84 red on both spinners is:
84/0.3= 280Probability of both spinners land on blue:
0.5*0.4= 0.2Estimated number of both spinners land on blue:
280*0.2= 56The estimated number of times that both spinners will land on blue is 56 times. This was calculated based on the number of times both spinners land on red and the probabilities of each spinner landing on blue.
Explanation:This problem deals with the subject of probability. Since we know that the number of times both spinners (A and B) land on red is 84, we can use this as a base to find the probability for each to land on blue.
The probability of spinner A landing on red is 0.5, therefore the probability of it landing on blue will also be 0.5 (1-0.5=0.5). Similarly, the probability of spinner B landing on red is 0.6, thus the probability of it landing on blue is 0.4 (1-0.6=0.4).
To get the overall probability of both spinners landing on blue, we multiply the probabilities for each individual spinner. Hence, the overall probability is 0.5 * 0.4 = 0.2.
Finally, to find the estimated number of times both spinners will land on blue, we can divide the number of times both spinners land on red (84) by the ratio of the probability for both landing on blue to the probability for both landing on red, yielding an estimate of 84 * (0.2 / 0.3) = 56 times.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ11
Find the measure of the angle indicated.
Answer:
110 degrees
Step-by-step explanation:
the angles are alternate exterior angles which means that they are the same
Answer:
110
Step-by-step explanation:
The angles are the same according to the corresponding angle postulate.
john made two candles in the shape of rectangular prisms. The first candle is 12cm high, 4 cm long, and 6 cm wide. The second candle is 4 cm higher, but has the same length and width. How much additional wax was needed to make the taller candle?
Answer:
96[tex]cm^3[/tex]
Step-by-step explanation:
To determine how much additional wax was needed to make the taller candle, we determine the volume of each of the candles and find the difference in their volumes
First Candle
Height=12cmLength=4 cmWidth= 6 cmVolume=Height X Length X Width
=12 X 4 X 6
=288[tex]cm^3[/tex]
Second Candle
The second candle is 4cm higher
Height=12+4=16cmLength=4 cmWidth= 6 cmVolume=Height X Length X Width
=16 X 4 X 6
=384[tex]cm^3[/tex]
Difference in Volume = 384-288 =96[tex]cm^3[/tex]
Therefore, 96[tex]cm^3[/tex] of additional wax was used to make the second candle.
a box contains 3 red marbles 6 blue marbles and 1 white marble. find the following probability. P(red and white and blue) without replacement
Answer:
3% unlikely
Step-by-step explanation:
if there are 10 marbles you can try to get 1 white, 1 blue, 1 red is't 3/10 = .3
Answer:
Blue 60%
Red 30%
White 10%
What are the coordinates of vertex F of parallelogram FGHJ?
(–2, 2)
(–2, 6)
(–3, 4)
(–4, 2)
Answer:
D (-4,2)
Step-by-step explanation:
The coordinates of F is (-4,2), the correct option is D.
What is a Parallelogram?A parallelogram is a polygon with four sides, the opposite sides of the parallelogram is equal and parallel.
The figure is attached with the answer.
The final image is obtained by series of Transformations
1. Translation (1,2)
Translation T₁,₂ is (x,y)→(x+1,y+2)
So, After translation from F to F' the point F' = (x+1,y+2)
2. After Reflection along y axis F" = (-(x+1), y+2)
F" = ( 3,4)
F' = (-3,4)
F = (-4 , 2)
Therefore, the coordinates of F is (-4,2), the correct option is D.
The missing figure is attached with the answer.
To know more about Paralleogram
https://brainly.com/question/14091538
#SPJ2
A bowling team participates in a two-day tournament and records the scores for each team member on both days. The scores for both days are represented by the box plots below.
A. The scores on Friday and the scores on Saturday have the same median and interquartile range.
B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.
C. The scores on Friday have a greater interquartile range than the scores on Saturday, but both data sets have the same median.
D. The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.
The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.
What is Median?The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Given data ,
From the given boxplot we can deduce the following points:
On Friday: Q₁ = 200, Q₂ = 215, Q₃ = 220 and IQR = 20.
On Saturday: Q₁ = 190, Q₂ = 205, Q₃ = 210 and IQR = 20.
And , the median of the data on Friday is M₁ = 220
And , the median of the data on Saturday is M₂ = 205
So , scores on Friday have a greater median than the scores on Saturday
Hence , the median is solved
To learn more about median click :
https://brainly.com/question/28687994
#SPJ3
The complete question is attached below :
A bowling team participates in a two-day tournament and records the scores for each team member on both days. The scores for both days are represented by the box plots below.
A. The scores on Friday and the scores on Saturday have the same median and interquartile range.
B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.
C. The scores on Friday have a greater interquartile range than the scores on Saturday, but both data sets have the same median.
D. The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.
Help me I’m new I’m in 8th
Answer:
14.1 in³
Step-by-step explanation:
Volume of sphere:
(4/3) × pi × r³
(4/3) × (22/7) × 1.5³
= 14.1428571426 in³
Answer:
14.1 cubic inch
Step-by-step explanation:
[tex]volume \: of \: knob \\ = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {1.5}^{3} \\ = \frac{4}{3} \times 3.14 \times 3.375 \\ = \frac{4}{3} \times 10.5975\\ = \frac{42.39}{3} \\ = 14.13 \: {inch}^{3} \\= 14.1 \: {inch}^{3} \\ [/tex]
i think of a number subtract three then multiply by four
Answer:
Step-by-step explanation:
To solve this
We have
Let the number think of b x
Three subtracted from the number will be
x-3
Then multiply by 4
4(x-3)
Open d brackets
4x-12
According to the given statement the expression will be "4x-12".
Let,
The number be "x".When "3" is subtracted from the number "x", we get
→ [tex]x-3[/tex]
and,
When "x-3" is multiply by "4", we get
→ [tex]4(x-3)[/tex]
After solving the brackets, we get
→ [tex]4x-12[/tex]
Thus the answer above is correct.
Learn more:
https://brainly.com/question/20726281
Help :( I suck at math
Answer:
D
Step-by-step explanation:
For some side lengths to create a triangle, any two of the side lengths must have an added length together of less than the third leg. Otherwise, the vertices would simply not be able to be connected by the lines. In a), 3+5=8, but since it is not more, the triangle will not be able to be formed (it would basically just be a line.) In B, 7+8< 16. In C, there is the same situation as with the first example (4+15=19). Finally, in the last one, 5+7>12, and all of the side lengths work out. Therefore, the correct answer is D. Hope this helps!
A person invests 9500 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12600 dollars?
To determine the time necessary for an investment to grow from $9,500 to $12,600 at an interest rate of 5.75% compounded quarterly, the compound interest formula is rearranged and solved for time, yielding approximately 6.6 years.
Explanation:To find out how long it takes for an investment to grow from $9,500 to $12,600 with an interest rate of 5.75% compounded quarterly, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per unit t.t is the time the money is invested for in years.In this case, we're solving for t, so we rearrange the formula: t = ln(A/P) / (n * ln(1 + r/n)). Substituting the provided values:
P = $9,500A = $12,600r = 0.0575 (5.75% expressed as a decimal)n = 4 (since interest is compounded quarterly)Thus, t = ln(12600/9500) / (4 * ln(1 + 0.0575/4)). After calculating, we find that t ≈ 6.6 years, rounded to the nearest tenth of a year.
The person must leave the money in the bank for approximately 5.4 years until it reaches $12600, with interest compounded quarterly.
To find out how long it takes for the investment to reach $12600 at a 5.75% interest compounded quarterly, we can use the formula for compound interest:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- A is the amount of money accumulated after t years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times interest is compounded per year.
- t is the time the money is invested for, in years.
We want to find t, so we can rearrange the formula to solve for t:
[tex]\[ t = \frac{\log\left(\frac{A}{P}\right)}{n \cdot \log\left(1 + \frac{r}{n}\right)} \][/tex]
Given:
- P = 9500
- A = 12600
- r = 0.0575 (5.75% expressed as a decimal)
- n = 4 (quarterly compounding)
Substituting these values into the formula:
[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + \frac{0.0575}{4}\right)} \][/tex]
[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + 0.0575/4\right)} \]\[ t \approx \frac{\log(1.32631579)}{4 \cdot \log(1.014375)} \]\[ t \approx \frac{0.12224324}{4 \cdot 0.00570388} \]\[ t \approx \frac{0.12224324}{0.02281552} \]\[ t \approx 5.361 \][/tex]
Rounded to the nearest tenth, it takes approximately 5.4 years for the investment to reach $12600 at 5.75% interest compounded quarterly.
What is the complete factorization of x2 + 4x - 45?
OOO
A. (x + 15)(x - 3)
OB. (x-9)(x + 5)
C. (x+ 9)(x - 5)
D. (x - 15)(x+3)
Answer: c
Step-by-step explanation:
[tex]x^2+4x-45[/tex]
[tex](x+9)(x-5)[/tex]
Answer:
c
Step-by-step explanation: