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]
Learn more about the simple interest here;
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What is the sum of the three solutions (find the values for x, y, and z, then add the answers)? 2x + 3y − z = 5 x − 3y + 2z = −6 3x + y − 4z = −8 Show All Work !!
Answer:
x + y + z = 4
Step-by-step explanation:
Give equations are,
2x + 3y - z = 5 --------(1)
x - 3y + 2z = -6 --------(2)
3x + y - 4z = -8 --------(3)
By adding equations (1) and (2),
(2x + 3y - z) + (x - 3y + 2z) = 5 - 6
3x + z = -1 -------(4)
By multiplying equation (3) by 3, then by adding to equation (2)
(9x + 3y - 12z) + (x - 3y + 2z) = -24 - 6
10x - 10z = -30
x - z = -3 --------- (5)
By adding equation (4) and (5),
(3x + z) + (x - z) = -1 - 3
4x = -4
x = -1
From equation (5),
-1 - z = -3
z = 2
From equation (1),
2(-1) + 3y - 2 = 5
-2 + 3y - 2 = 5
3y = 5 + 4
y = 3
Therefore, x + y + z = -1 + 3 + 2
x + y + z = 4
plz help me. how many solutions
Answer:
no solutions
Step-by-step explanation:
2y = 4x+6
y = 2x+6
Divide the first equation by 2
y = 2x+3
These are parallel lines ( same slope) but different y intercepts
They will never intersect, so they have no solutions
Answer:
B No solutions
Step-by-step explanation:
2y = 4x + 6 first equatión
y = 2x + 6 second equation
from the first equation
y = (4x+6)/2
y = 4x/2 + 6/2
y = 2x + 3 third equation
matching second equatión and third equation
2x + 6 = 2x + 3
2x - 2x = 3 - 6
0 ≠ -3
then:
Β No solutions
Helppp thank you!!!!!
Answer:
D
Step-by-step explanation:
x is greater than 12:
[tex]x>12 \text{ or } 12<x[/tex]
and x is less than or equal to 3 times the value of y:
[tex]12<x\leq 3y[/tex]
We can divide everything by 3:
[tex]4<\frac{x}{3} \leq y[/tex]
A group of friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves
Complete question:
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Check all that apply. The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill. The equation 1/8 (x+16)=76 represents the situation, where x is the food bill. The solution x=60 represents the total food bill. The solution x=60 represents each friend’s share of the food bill and tip. The equation 8(x+16)=76 represents the situation, where x is the food bill.
Answer:
The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill
The solution x=60 represents the total food bill
Step-by-step explanation:
Given the following :
Total amount spent = $76
Amount paid as tip = $16
Number of friends = 8
Total Cost of lunch consists of:
Actual Cost of food + amount of tip
Let actual cost of food = x
Total cost of lunch is thus :
x + $16 = $76
If the friends are to each the bill equally:
Then:
Divide both sides by 8:
(1/8)* (x + 16) = 76/8
Therefore,
(x + 16) / 8 = 76/8
x + 16 = 76 / 8
(x + 16)/8 = 9.5
x + 16 = 9.5 * 8
x + 16 = 76
x = 76 - 16
x = 60
Answer:
A
and
C
Step-by-step explanation:
match each polynomial with its degree
degree 1
degree 2
degree 3
degree 4
a.8x^2+7+1/2x^3-3 (1/2 is a fraction)
b.3x^2-2x+4
c.(x^2)^2+(x+4)^2
d.5x+5
Answer:
d
b
a
c
Step-by-step explanation:
degree 1 - 5x+5 - d.
degree 2- 3x^2-2x+4- b.
degree 3 - 1/2x^3+8x^2-3- a.
degree 4 - x^4+(x+4)^2- c
FACTOR THIS EXPRESSION -385y LOOK AT THE SCREENSHOT THANKS AND BRAINLIST IF CORRECT PLEASE HELP
Answer:
-1*5*7*11*y
Step-by-step explanation:
This is the prime factorization of 385y times -1.
Please Help Me With This I Will Mark Brainliest If You Are Correct!!!!!!!!!!! Determine the intervals on which the function is increasing, decreasing, and constant. A coordinate axis is drawn with a parabola pointing up that has vertex of 0,3. A). Increasing x 0 B). Increasing x > 0; Decreasing x 3 D). Increasing x > 3; Decreasing x < 3
Answer:
Increasing x> 3
Decreasing x< 3
Step-by-step explanation:
If you imagine drawing a tangent line (a line which touches a curve or shape at one point) at some point on the graph, you can see if a curve is increasing or decreasing at that point; and on the whole interval.
Doing this I find that the curve is decreasing on x< 3 and increases on x> 3
n/8 = (-7) help please
Answer:
n = -56
Step-by-step explanation:
n/8 = (-7)
Multiply each side by 8
n/8* 8 = (-7)*8
n = -56
Answer:
[tex]n=-56[/tex]
Step-by-step explanation:
We can use algebra and simplify the equation until we have n isolated.
[tex]\frac{n}{8} = -7\\\frac{n}{8}\cdot8 = -7\cdot8\\\\n=-56[/tex]
Hope this helped!
u and v are position vectors with terminal points at (-8, 5) and (-3, -12), respectively. Find the terminal point of u + v
(-11, -7)
(-11, 7)
(-5, -7)
(5, -17)
Answer:
(-11,-7)
Step-by-step explanation:
U V
(-8,5) + (-3,-12)
(-8 - 3) , (5 - 12)
-11 , -7
(-11,7)
Answer:
(-11,-7)
Step-by-step explanation:
u = (-8, 5)
v = (-3, -12)
u+v = ( -8+-3, 5+-12)
= (-11,-7)
Find the value of x in the figure below.
A. 25
B. 35
C. 45
D. 65
Answer:x=45
Step-by-step explanation:
Gary is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below:
A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line.
He starts with the assumption that segment DE is parallel to segment BC.
Which inequality will he use to contradict the assumption?
Answer:
That Ratios aren't equal.
Step-by-step explanation:
Given: DE is || to BC.
So in order to make this false then we have to say that the sides aren't proprtional, making it not possible to get the ratios equal.
(See the Triangle proprtionality theorem or the triangle midsegment theorem)
Answer:
4:10 ≠ 6:14
Step-by-step explanation:
bc i said so
7. Consider a topograph with values 1,7,-2 as in the margin (pictured).
Fill in the ?s to satisfy the arithmetic progression rule
Answer:
see below
Step-by-step explanation:
The "arithmetic progression rule" requires the numbers on either side of an edge make an arithmetic progression with the numbers at either end.
If we label the variables 'a', 'b', 'c' clockwise from top, then the rule means we have ...
2a -b +2c = 1
2a +2b -c = 7
-a +2b +2c = -2
Solution
Adding twice the second equation to each of the other two gives ...
2(2a +2b -c) +(2a -b +2c) = 2(7) +(1)
6a +3b = 15 . . . . [eq4]
and
2(2a +2b -c) +(-a +2b +2c) = 2(7) +(-2)
3a +6b = 12 . . . . [eq5]
Subtracting [eq5] from twice [eq4] we have ...
2(6a +3b) -(3a +6b) = 2(15) -(12)
9a = 18
a = 2
From [eq4], we can find b:
b = (15 -6a)/3 = 5 -2a = 5 -2(2) = 1
From [eq2] we can find c:
c = 2(a+b) -7 = 2(2+1) -7 = -1
These values are shown on the diagram below.
ABCD is a parallelogram. Find the values of x and y. Solve for the value of z, if z = x - y.
A
B
(x+30)° (x-30)
(y+20)
D
С
Answer:
(x+30)+(x-30)=180
2x=180
x=90
x+30=y+20
90+30=y+20
y=100°
There for z = -10
Simplify the following expression.
Answer:
3x+11y-3
Step-by-step explanation:
Hey! So here is what you do to solve the problem-
Combine like terms:
(x) 5x-2x=3x
(y) 3y+8y=11y
(#) 7-10 =-3
So....
3x+11y-3 is your answer!
Hope this helps!:)
Solve for x and draw a number line. 3x−91>−87 AND 17x−16>18
Answer:
I hope this will help!
Step-by-step explanation:
Jermiah answer 90% of the questions on his test correctly. There are 40 questions on the test
Answer:
36 answered correctly
Step-by-step explanation:
Hey there!
Well 90% of 40 is 36.
This is true because 90% as a fraction not simplified is 36/40 and when we do,
36 ÷ 40 we get .9.
And we move the decimal places 2 times to the right in .9 and we get 90%.
Hope this helps :)
Answer:
36
Step-by-step explanation:
I need help pls and I will give a 5 star rating and a big thank you comrades.
Answer:
Option (C) : y = 6 / 11
Step-by-step explanation:
To find Horizontal Asymptote of the function, you need to see degree of of numerator and denominator.
Since, the degrees of the numerator and denominator are the same,
Horizontal Asymptote = leading coefficient of the numerator divided byleading coefficient of the denominator
Therefore,
Horizontal Asymptote = 6 / 11
What is the following product? StartRoot 12 EndRoot times StartRoot 18 EndRoot StartRoot 30 EndRoot
Answer:
[tex] 6\sqrt{6} [/tex]
Step-by-step explanation:
[tex] \sqrt{12}\sqrt{18} = [/tex]
[tex] = \sqrt{12 \cdot 18} [/tex]
[tex] = \sqrt{4 \cdot 3 \cdot 9 \cdot 2} [/tex]
[tex] = \sqrt{36 \cdot 6} [/tex]
[tex] = \sqrt{36}\sqrt{6} [/tex]
[tex] = 6\sqrt{6} [/tex]
Following are the step by step solutions to the given expression:
Given:
[tex]\to \sqrt{12} \times \sqrt{18} \sqrt{30}[/tex]
To find:
solve=?
Solution:
[tex]\to \sqrt{12} \times \sqrt{18} \sqrt{30}[/tex]
[tex]\to \sqrt{2\times 2 \times 3} \times \sqrt{2\times 3 \times 3} \sqrt{2 \times 3 \times 5} \\\\ [/tex]
[tex]\to 2\sqrt{3} \times 3\sqrt{2} \sqrt{2 \times 3 \times 5} \\\\ \to 6\times \sqrt{3} \times \sqrt{2} \sqrt{2\times 3 \times 5} \\\\ \to 6\times \sqrt{3} \times \sqrt{2} \times \sqrt{2}\times \sqrt{3} \times \sqrt{5} \\\\ \to 6 \times 3 \times 2 \times \sqrt{5} \\\\ \to 36 \sqrt{5}[/tex]
Therefore, the final answer is "[tex]36\sqrt{5}[/tex]"
Learn more:
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m∠QPSm, is a straight angle m∠RPS=6x+11 m∠QPR=7x+143 ;Find RPS
Answer:
23
Step-by-step explanation:
6x + 11 + 7x + 143 = 180
13x + 154 = 180
13x = 26
x = 2
m<RPS = 6(2) + 11 = 23
he blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4
Answer:
The approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
Step-by-step explanation:
We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7.
Let X = the blood platelet counts of a group of women
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 247.3
[tex]\sigma[/tex] = standard deviation = 60.7
Now, according to the empirical rule;
68% of the data values lie within one standard deviation of the mean.95% of the data values lie within two standard deviations of the mean.99.7% of the data values lie within three standard deviations of the mean.Since it is stated that we have to calculate the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4, i.e;
z-score for 65.2 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{65.2-247.3}{60.7}[/tex] = -3
z-score for 429.4 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{429.4-247.3}{60.7}[/tex] = 3
So, it means that the approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
What is m
Round the answer to the nearest whole number.
O 30°
O 35°
O 55°
O 60°
Answer:
30
Step-by-step explanation:
fufyfuf7fjcjcufuy7fufucyyxyvkbuvufudydy shut up
help with this you guys i know im asking to many questions and sorry because im going to keep asking them.
D is your answer please like this answer
with a tax rate of 0.0200, a tax bill of 1050 corresponds to an assessed valuation of
Answer:
$52,500
Step-by-step explanation:
1050/0.0200=52500
Answer:
B. 52,500
Step-by-step explanation:
WILL GIVE BRAINLIEST
intercept is the length from origin to intersection point of respective axis,
it intersects x axis at -7.5 and y is 0 so x intercept is (-7.5,0)
and similarly, y intercept is (0,5.5)
Answer:
(- 7.5, 0 ) and (0, 5.5 )
Step-by-step explanation:
The x- intercept is the value of x on the x- axis where the line crosses.
Here the line crosses the x- axis at - 7.5 , thus the coordinates of x- intercept
(- 7.5, 0 )
The y- intercept is the value of y on the y- axis where the line crosses.
Here the line crosses the y- axis at 5.5 thus the coordinates of the y- intercept
(0, 5.5 )
Solve: 5x2 + 25x = 0
Answer:
x = -0.4
x = -(2/5)
Answer:
x = ± √5
Step-by-step explanation:
Please indicate exponentiation by using the symbol " ^ ":
5x^2 + 25x = 0
Divide all three terms by 5. We get:
x^2 + 5 = 0, or x^2 = -5
Then x = ± √5
If the sphere shown above has a radius of 17 units, then what is the approximate volume of the sphere?
A.
385.33 cubic units
B.
4,913 cubic units
C.
6,550.67 cubic units
D.
3,275.34 cubic units
Answer:
20582.195 unitsStep-by-step explanation:
This problem is on the mensuration of solids.
A sphere is a solid shape.
Given data
radius of sphere = 17 units
The volume of a sphere can be expressed as below
[tex]volume = \frac{4}{3}\pi r^3[/tex]
Substituting our data into the expression we have
[tex]volume = \frac{4}{3}*3.142*17^3[/tex]
[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]
The volume of the sphere is given as
20582.195 units
What is the exponential form of log9 5 = y
Answer:
y = 0.732
Step-by-step explanation:
log3²(5) = y
(1/2) × log3(5) = y
y = (1/2) × log3(5)
y = 0.732487
y = 0.732 ( 3 sig.fig )
john always wears a shirt, pants, socks, and shoes. he owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. how many different outfits can john make? PLEASE ANSWER
Answer:
900 outfits
Step-by-step explanation:
You just have to multiply them all together :)
What’s up guys, pls help 19b)
Thanks
Answer:
90°
Step-by-step explanation:
As given in the figure:
[tex]AC \perp CE\\
\therefore m\angle ACE = 90\degree \\ [/tex]
Write down inequalities,that are satisfied by these sets of integers between -10 and 10
1,2,3,4,5,6,7,8,9,10
-3,-4,-5,-6,-7,-8,-9,-10
9,10
-10
Answer:
Below
Step-by-step explanation:
Notice that x is between 10 and -10 but takes only the values that are integers.
The inequalities:
● we can write an inequality that includes all these values.
● -10 《 x 《 10
This is a possible inequality
Multiply both sides by 2 and you will get a new one:
● -20 《 2x 《 20
You can multiply it by any number to generate a new inequality.
Or you can add or substract any number.
