Answer:
→To combine the two functions, you have to multiply them together, like so:
h(x) · s(x)
→This can also be shown as:
[tex](103)(1.03)^x^-^1[/tex]
The reason as to why you would multiply the two functions together, and not add, is because of the words accrues. Based on the information given, the interest amount of money, which is $103, accrues, which basically means that the money will increase in a pattern, over time. In addition, when a world problem involves a bank and money, multiplication is usually occurring.
The total amount of money Christina will have in her bank account as interest accrues after she deposits her $103 is g(x) = (103)(1.03)^(x-1).
What is simple interest?Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.
Christina has $103 earned from babysitting saved at home, and the amount is modeled by the function,
[tex]h(x) = 103[/tex]
She reads about a bank that has savings accounts that accrue interest according to the function,
[tex]s(x) = (1.03)^{(x-1)}[/tex]
This function means that the interest amount is 3% in value per year in which x represent the number of years.
Now the total amount of money she will have in her bank account as interest accrues will be equal to the product principal and interest rate.
Let the amount of money she will have in her bank account as interest accrues is represented by function g(x). Thus,
[tex]g(x) = (103)(1.03)^{(x-1)}[/tex]
Thus, the total amount of money Christina will have in her bank account as interest accrues after she deposits her $103 is.
[tex]g(x) = (103)(1.03)^{(x-1)}.[/tex]
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If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answer:
7800 brownies will be produced in an 8 hour shift
Step-by-step explanation:
Given : The production rate is 975 brownies per hour at a bakery
To Find : how many brownies will be produced in an 8 hour shift?
Solution:
No. of brownies produced in 1 hour = 975
We are supposed to find No. of brownies produced in 8 hour
No. of brownies produced in 8 hour = 975 x 8=7800
Hence 7800 brownies will be produced in an 8 hour shift
Hope this helps ФωФ
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer: will be A
Step-by-step explanation:
Mary spent $45 at the mall. She bought lunch for $9. She bought 3 shirts at
each. Which of the following equations could be used to find x ?
Answer:
x = 12
Step-by-step explanation:
If Mary spent $45 altogether,
then she bought lunch for $9
so our equation now is
$45 = $9 + 3x
It is 3x because he bought 3 shirts and we used x because we didnt
now how much the price of those shirts were
$45 = $9 +3x
$45 - $9 = 3x
$45 - $9 = $36
$36 = 3x
$36 / 3 = 12
x = 12
Please mark this answer as the brainliest
How do I write a verbal expression for each algebraic expression?
23f
Answer:
Twenty three times f
Step-by-step explanation:
Given 4,7,10,13. Determine a rule to describe the general term, Tn.
Answer:
[tex]T_{n}[/tex] = 3n + 1
Step-by-step explanation:
There is a common difference between consecutive terms, that is
7 - 4 = 10 - 7 = 13 - 10 = 3
This indicates the sequence is arithmetic with nth term
[tex]T_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 4 and d = 3 , then
[tex]T_{n}[/tex] = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1
Simplify 18-2[x + (x - 5)].
O8-4x
28 - 4x
28 - 2x
Answer:
28-4x
Step-by-step explanation:
Step 1: Open most inner bracket and simplify
=18-2(x+x-5)
=18-2(2x-5)
Step 2: Expand brackets by multiplying 2 in and simplify
=18-2(2x)-2(-5)
=18-4x+10
=28-4x
Therefore the answer is 28-4x
Wo commondities A and B cost 070 and D80 respe
with 26 kg of B and the mixture issold at 085 per kg: calo
The weight (in kg) of 50 contenstants at a competition is
65 66 67 66 64 66 65 63 65 68
64 62 66 64 67 65 64 66 65 67
65 67 66 64 65 64 66 65 64 65
66 65 64 65 63 63 67 65 63 64
66 64 68 65 63 65 64 67 66 64
a. construct a frequency table for the discrete data
b. calculate, correct to 2 decimal places, the
mean,
ii. standard deviation of the data
Answer:
b) 65.08
ii) 0.75
Step-by-step explanation:
x(Kg): 62 63 64 65 66 67 68
Frequency(f): 1 5 11 15 10 6 2
xf: 62 315 704 975 660 402 136
b) mean(X) = ∑xf/N = 3254/50 = 65.08
c) x - X : -3.08 -2.08 -1.08 -0.08 0.92 1.92 2.92
(x - X)²: 9.49 4.33 1.17 0.0064 0.85 3.69 8.53
ii) Standard deviation(S.D.): √(∑(x - X)²/N = √(28.0664)/50 = √0.5613
∴ S.D.= 0.75
Geometry, please answer my question ASAP
Answer:
98 degrees
Step-by-step explanation:
The angles of a quadrilateral add up to 360 degrees, therefore:
(25x+1)+(25x-2)+(20x-1)+82=360
70x +80=360
70x=280
x=4
the angle at C:
25*4-2 = 98 degrees
I WILL GIVE U BRAINLIST AND A THANK YOU PLS ANDWER!!!!!!!!!
Answer:
yes it is proportional because you don't buy the popcorn
Answer:
A. Yes.
Step-by-step explanation:
Since you never buy popcorn, the only thing you buy are movie tickets. The only thing contributing to the total price are the movie tickets, so the total price is proportional to the number of movie tickets purchased.
Hope this helps!
lowkey need help with this.
9514 1404 393
Answer:
c = 14
no extraneous solutions
Step-by-step explanation:
You can subtract the right-side expression, combine fractions, and set the numerator to zero.
[tex]\dfrac{c-4}{c-2}-\left(\dfrac{c-2}{c+2}-\dfrac{1}{2-c}\right)=0\\\\\dfrac{c-4}{c-2}-\dfrac{1}{c-2}-\dfrac{c-2}{c+2}=0\\\\\dfrac{(c-5)(c+2)-(c-2)^2}{(c-2)(c+2)}=0\\\\\dfrac{(c^2-3c-10)-(c^2-4c +4)}{(c-2)(c+2)}=0\\\\\dfrac{c-14}{(c-2)(c+2)}=0\\\\\boxed{c=14}[/tex]
__
Check
(14 -4)/(14 -2) = (14 -2)/(14 +2) -1/(2 -14) . . . . substitute for c
10/12 = 12/16 -1/-12
5/6 = 3/4 +1/12 . . . . true
There is one solution (c=14) and it is a solution to the original equation. There are no extraneous solutions.
If a quadratic equation is written in intercept form, y = (x-3)(x+5), then vertex is at...
Answer:
The vertex is at (-1, -16).
Step-by-step explanation:
We are given the quadratic equation:
[tex]y = (x-3)(x+5)[/tex]
And we want to find its vertex.
Recall that the x-coordinate of the vertex is also the axis of symmetry. Since a parabola is symmetric about the axis of symmetry, the axis of symmetry is halfway between the two roots.
From the equation, we can see that our two roots are x = 3 and x = -5.
Hence, the axis of symmetry or the x-coordinate of the vertex is:
[tex]\displaystyle x = \frac{(3) + (-5)}{2} = -1[/tex]
To find the y-coordinate of the vertex, evaluate the equation at x = -1:
[tex]\displaystyle \begin{aligned} y(-1) &= ((-1)-3)((-1)+5)\\ &= (-4)(4) \\&= -16\end{aligned}[/tex]
Hence, the vertex is at (-1, -16).
The function f is defined by the following rule
f (x) - 5+1
Complete the function table.
-5
-1
0
2
3
Answer:
The answer to your question is given below.
Step-by-step explanation:
1. f(x) = 5x + 1
x = – 5
f(x) = 5x + 1
f(–5) = 5(–5) + 1
f(–5) = –25 + 1
f(–5) = –24
2. f(x) = 5x + 1
x = – 1
f(x) = 5x + 1
f(–1) = 5(–1) + 1
f(–1) = –5 + 1
f(–1) = – 4
3. f(x) = 5x + 1
x = 1
f(x) = 5x + 1
f(1) = 5(1) + 1
f(1) = 5 + 1
f(1) = 6
4. f(x) = 5x + 1
x = 2
f(x) = 5x + 1
f(2) = 5(2) + 1
f(2) = 10 + 1
f(2) = 11
5. f(x) = 5x + 1
x = 2
f(x) = 5x + 1
f(3) = 5(3) + 1
f(3) = 15 + 1
f(3) = 16
Summary
x >>>>>>>> f(x)
–5 >>>>>> – 24
–1 >>>>>> – 4
1 >>>>>>>> 6
2 >>>>>>> 11
3 >>>>>>> 16
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 31 31 beats per minute, the mean of the listed pulse rates is x overbar x equals = 71.0 71.0 beats per minute, and their standard deviation is s equals = 12.6 12.6 beats per minute.
Complete question is;
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 31 beats per minute, the mean of the listed pulse rates is x over bar equals 71.0 beats per minute, and their standard deviation is s equals 12.6 beats per minute.
a. What is the difference between the pulse rate of 31 beats per minute and the mean pulse rate of the females?
b. How many standard deviations is that [the difference found in part (a)]?
c. Convert the pulse rate of 31 beats per minutes to a z score.
d. If we consider pulse rates that convert to z scores between minus 2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 31 beats per minute significant?
Answer:
A) 40 beats per minute
B) 3.1746
C) z = -3.17
D) the pulse rate of 31 beats per minute is significantly low.
Step-by-step explanation:
A) The mean pulse rate is given as x bar = 71
Thus difference between this and pulse rate of 31 beats per minute is;
Difference = 71 - 31 = 40 beats per minute
B) number of standard deviations of the difference found in part a is given as;
number = difference/standard deviation(s)
number = 40/12.6
number = 3.1746
C) The z-score is calculated from;
z = (x - xbar)/s
z = (31 - 71)/12.6
z = -3.17
D) from the question we are told that the z scores between minus2 and 2 to be neither significantly low nor significantly high. However, we have a Z-score of -3.17 which doesn't fall into that range. Thus, the pulse rate of 31 beats per minute is significantly low.
Help me with this question please‼️‼️
Explanation:
The gradient is the same as the slope
m = slope
m = rise/run
m = (change in y)/(change in x)
m = (y2-y1)/(x2-x1)
m = (6-1)/(6 - (-4))
m = (6-1)/(6+4)
m = 5/10
m = 1/2
In decimal form, this becomes 0.5
A slope of 1/2 means we move up 1 and to the right 2 units each time to generate points along the diagonal line.
A positive slope goes uphill as we move to the right (due to the positive rise value).
Answer:
One way to find the gradient is using the expression :
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{y_{B} - y_{A}}{x_{B} - x_{A}}[/tex]
So [tex]m = \frac{6 - 1}{6- (-4)} =\frac{5}{10} =\frac{1}{2}[/tex]
(3)/(22)+(-(1)/(11) find the sum without use of a number line
Answer:
1/22
Step-by-step explanation:
Simplify it.
It becomes 3/22-1/11
Change the denominator to 22 becasue that is the LCM.
It becomes 3/22-2/22 which is 1/22. :)
Does 8in to 1ft reduce it or enlarge it
Answer:
enlarge it
Step-by-step explanation:
I ft = 12 inches
Thus 8 in → 12 in makes the transformation larger.
Thus going from 8 in to 12 in is an enlargement
A biology class has a total of 35 students. The number of females is 11 less than the number of males. How many males and how many females are in the class?
Answer:
23 males and 12 females
Step-by-step explanation:
x = # of females
y = # of males
x + y = 35
x + x + 11 = 35
2x + 11 =35 (SUBTRACT 11 FROM BOTH SIDES)
2x = 24 (DIVIDE BOTH SIDES BY 2)
x = 12 females
x + y =35
12 + y = 35 (SUBTRACT 12 FROM BOTH SIDES)
y = 23 males
23 males + 12 females = 35 students
S=n/2(2a+(n-1)d). If d=5, n=13, S=585 find the value of a.
Answer:
15
Step-by-step explanation:
Sum of 'n' terms formula is given by:-
s=n/2(2a+(n-1)d)
s=13/2[2xa+(13-1)5]
s=13/2(2xa+12x5)
s=13/2(2a+60)
585=13/2(2a+60)
585 x (2/13) = 2a + 60
90 = 2a + 60
90-60 = 2a
30 = 2a
a = 15
Both please please :)…….,,,,,
Answer:
Step-by-step explanation:
One - 44
88% of 50 is 44
Two - 55296 60,000-4%-4%=55296
which is a true statement about an exterior angle of a triangle
Answer:
D
Step-by-step explanation:
The exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.
The pair also rests on the same flat/straight line and that makes a pair.
Therefore we can say that it is formed by a linear pair/group with one of the interior/inside angles of the triangle.
So, the correct answer would be D.
The true statement about an exterior angle of a triangle is C; It forms a linear pair with one of the interiior angles of the triangle .
What is the Exterior Angle of a Triangle Property?An exterior angle of a triangle is equal to the sum of the opposite interior angles.
We know that the exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.
The pair also rests on the same straight line and that makes a pairs.
Therefore we can say that it is formed by a linear pair with one of the interior angles of the triangle.
So, the correct answer would be C.
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Complete the table. At least the first few so I understand how to do it
Answer:
What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36
Please check explanation for complete answer
Step-by-step explanation:
Here, we are concerned about filling the empty columns of the table.
What we want to do here is simply straightforward. All we need to do is to
multiply the values of x by the values of P(x) in each of the individual rows.
Also recall, we do not need to reduce the fractions.
So we have;
2. 3 * 2/36 = 6/36
3. 4 * 3/36 = 12/36
4. 5 * 4/36 = 20/36
5. 6 * 5/36 = 30/36
6. 7 * 6/36 = 42/36
7. 8 * 5/36 = 40/36
8. 9 * 4/36 = 36/36
9. 10 * 3/36 = 30/36
10. 11 * 2/36 = 22/36
11. 12 * 1/36 = 12/36
Mary wants to get spray foam insulation in her attic space. Shown here is a diagram of her attic - how much spray foam does she need to buy
Answer:
455
Step-by-step explanation:
(1/2(10)(70))13
Mary needs to buy [tex]455~m^3[/tex] spray foam.
The correct answer is an option (B)
What is the volume of the triangular prism?"Volume = base area × length,
where, Base area = area of triangle
Length = length(or height) of the triangular prism"
For given question,
Mary wants to get spray foam insulation in her attic space.
To find the amount of spray foam she needs to buy, we need to find the volume of the given triangular prism.
First we find the base area of the given triangular prism.
For a triangular base,
base = 7 m and height = 10 m
Using the formula of the area of the triangle,
[tex]A=\frac{1}{2}\times 7\times 10\\\\ A=7\times 5\\\\A=35~sq.m.[/tex]
Now, we find the volume of the triangular prism.
[tex]V=A\times l\\\\V=35\times 13\\\\V=455~m^3[/tex]
Therefore, she needs to buy [tex]455~m^3[/tex] spray foam.
The correct answer is an option (B)
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If the distance between the points (2, -2) and (-1, x) is 5, one of the values of x is
We know
[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
ATQ
[tex]\\ \sf\longmapsto \sqrt{(-1-2)^2+(x+2)^2}=5[/tex]
[tex]\\ \sf\longmapsto \sqrt{(-3)^2+x^2+4x+4}=5[/tex]
[tex]\\ \sf\longmapsto \sqrt{9+x^2+4x+4}=5[/tex]
[tex]\\ \sf\longmapsto \sqrt{x^2+4x+13}=5[/tex]
[tex]\\ \sf\longmapsto x^2+4x+13=5^2=25[/tex]
[tex]\\ \sf\longmapsto x^2+4x+13-25=0[/tex]
[tex]\\ \sf\longmapsto x^2+4x-12=0[/tex]
[tex]\\ \sf\longmapsto x^2+6x-2x-12=0[/tex]
[tex]\\ \sf\longmapsto x(x+6)-2(x+6)=0[/tex]
[tex]\\ \sf\longmapsto (x-2)(x+6)=0[/tex]
[tex]\\ \sf\longmapsto x=2\:or\:x=-6[/tex]
Select the answer choice that is equivalent to the expression given belon.
9(2x - 3) + 5y + 17
0) O-4% - 10
O 23% - 10
0 0 -4% + 17
0 0 -49% + 17
O 16% + 23
Answer:
[tex] 23x - 10 [/tex]
Step-by-step explanation:
To the find the equivalent of [tex] 9(2x - 3) + 5x + 17 [/tex], evaluate the expression. Start by opening the bracket.
[tex] 9*2x - 9*3 + 5x + 17 [/tex]
[tex] 18x - 27 + 5x + 17 [/tex]
Pair like terms
[tex] 18x + 5x - 27 + 17 [/tex]
[tex] 23x - 10 [/tex]
The equivalent of [tex] 9(2x - 3) + 5x + 17 [/tex] is [tex] 23x - 10 [/tex]
find the surface area of the cylinder and round to the nearest tenth
Answer: A = 833.66 in^2
Step-by-step explanation:
Area of the base = (7^2)(pi) = 49 pi = 153.9 in^2
Height of the cylinder = 12 in
Circumference of the base = (2)(pi)(r) = 44in
Surface area = (2)(pi)(7)(12) + (2)(pi)(7) = 833.66 in^2
PLEASEEEEEEE HELP with this question
Answer:
second table
Step-by-step explanation:
Out of the 8 options on the spinner, 2 of them are 0's, 1 of them is a 1, 2 of them are 2's and 3 of them are 3's so the probability of spinning a 0, 1, 2 or 3 is 2/8, 1/8, 2/8 or 3/8 which becomes 0.25, 0.125, 0.25 or 0.375 respectively. Therefore, the answer is the second table.
How does a globe represent the fact that there are no parallel lines in elliptical geometry? A. The equator is not parallel to any other latitudinal lines. B. The north and south poles are never connected by a geodesic. C. The geodesics connecting the Nortj and South poles never intersect. D. The geodesics connecting the north and south poles intersect at both of the poles.
Answer:
The correct option is;
D. The geodesics connecting the North as South poles intersect at both of the poles
Step-by-step explanation:
As an analog to the straight line, the geodesic of a curved surface is the shortest path between two points on the curved surface
Whereby the Earth is assumed to be spherical, the geodesics around the Earth would then be closed circles and like the longitude and latitude, will meet at the North and South poles
However given that the Earth is an Oblate ellipsoid, Euclid's parallel postulate is not in effect and the geodesics connecting the North and South Poles Intersect at both poles.
The answer is Option D, option D is correct.
BRAINLIEST, THANKS AND 5 STARS IF ANSWERED BOTH CORRECTLY. What is the 7th term in this geometric sequence? 3, 12, 48, 192.. ---------- What is the ratio (multiplier) of the following geometric sequence? 4, 2, 1, 0.5
Answer:
see below
Step-by-step explanation:
3, 12, 48, 192
We are multiplying by 4 each time (12/3 =4)
The 5th term
192 *4 =768
The 6th term
768 *4 =3072
The th term
3072 *4 =12288
To find the common ratio, take the second term and divide by the first
2/4 = 1/2
The common ratio is 1/2
Problem 1
Answer: 12288---------------------------
Explanation:
The first term is a = 3 and the common ratio or multiplier is r = 4. We start with 3 and multiply each term by 4 to get the next one. The nth term of this geometric sequence is
a(n) = a*(r)^(n-1)
a(n) = 3*(4)^(n-1)
Plug in n = 7 to get the seventh term
a(7) = 3*(4)^(7-1)
a(7) = 3*(4)^6
a(7) = 3*4096
a(7) = 12288
====================================================
Problem 2
Answer: 1/2 or 0.5----------------------
Explanation:
To find the common ratio, we pick any term but the first one and divide it over its previous term
r = common ratio
r = (second term)/(first term) = 2/4 = 1/2 = 0.5
r = (third term)/(second term) = 1/2 = 0.5
r = (fourth term)/(third term) = 0.5/1 = 0.5
Each term is cut in half to get the next one.
solve for each of the following equations. /2x+3/=10
Answer:
/2x+3/=10
2x+3=10 or 2x+3=-10
2x=10-3 or 2x=-10-3
2x=7 or 2x=-13
X=7÷2 or X=-13÷2
X=3.5 or X=-6.5
Given that MTW = CAD, which segments are corresponding parts of the congruent triangles? MT CD MW CA TW. AD
Answer:
TW correspondant to AD
Step-by-step explanation:
That's the right answer
Segments TW and AD are corresponding parts of the congruent triangles.
What are congruent triangles?Two triangles are called congruent if their corresponding sides and angles are congruent.
Given that, Δ MTW ≅ Δ CAD
The congruent parts are;
MT = CA
TW = AD
MW = CD
∠ M = ∠ C
∠ T = ∠ A
∠ W = ∠ D
Hence, Segments TW and AD are corresponding parts of the congruent triangles.
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