a home improvement store charges $20 to rent a small truck for 1 hour . Each additional hour costs $25 . There is also a fuel surcharge of $0.05 for each mile driven .How much will it cost to rent the truck for 4 hours if it is driven 30 miles
Answer:
It will cost $121.50
Step-by-step explanation:
C = 20 + 25h + .05m
Now plug in the hours and miles
C = 20 + 25(4) + .05(30)
C = 20 + 100 + 1.5
C = 121.50
The total cost rent the truck for 4 hours and 30 miles drive is $121.5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Given that, a home improvement store charges $20 to rent a small truck for 1 hour.
Let the number of hours be h and the number of miles be m.
Now, total charge = 20+25h+0.05m
Here, h=4 and m=30
So, total charge = 20+25(4)+0.05(30)
= $121.5
Therefore, the total cost rent the truck for 4 hours and 30 miles drive is $121.5.
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Solve for m.
13 =2m+513=2m+5
Answer:
m=13
Step-by-step explanation:
What is the answer
To celebrate 24 years in business, a clothing store's marketing executive is ordering scratch-off discount coupons to give to customers. She would like 40% of customers in the population to receive the highest possible discount, with an SEP of 0.01 for this population. How many coupons should she order?
Answer:
She should order 2400 coupons.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
She would like 40% of customers in the population to receive the highest possible discount, with an SEP of 0.01 for this population.
This means that [tex]p = 0.4, s = 0.01[/tex]
How many coupons should she order?
We have to find n. So
[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]0.01 = \sqrt{\frac{0.4*0.6}{n}}[/tex]
[tex]0.01\sqrt{n} = \sqrt{0.4*0.6}[/tex]
[tex]\sqrt{n} = \frac{\sqrt{0.4*0.6}}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{\sqrt{0.4*0.6}}{0.01})^2[/tex]
[tex]n = 2400[/tex]
She should order 2400 coupons.
100 points Which expression represents the following calculation?
Subtract 32 from the product of 48 and 15.
A. 32 – (48 × 15)
B. (48 – 15) × 32
C. (48 × 15) – 32
D. 32 × (48 – 15)
Please quick
Answer:C
Step-by-step explanation: you have to multiply first than subtract because it says subtract 32 FROM the product meaning multiplying comes first than subtract
Use the drawing tools to form the correct answer on the graph.
Graph the line that represents this equation:
3x-4y=8
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]3x - 4y = 8[/tex]
Required
Graph the line
First, we calculate the intercepts
Set x = 0
So:
[tex]3x - 4y = 8[/tex]
[tex]3*0 - 4y = 8[/tex]
[tex]- 4y = 8[/tex]
Divide by -4
[tex]y = -2[/tex]
So, we have:
[tex](x,y) = (0,-2)[/tex]
Next, set y = 0
So:
[tex]3x - 4y = 8[/tex]
[tex]3x - 4 * 0 = 8[/tex]
[tex]3x = 8[/tex]
Divide by 3
[tex]x = 8/3[/tex]
So, we have:
[tex](x,y) = (8/3,0)[/tex]
The graph to be plotted must pass through [tex](x,y) = (0,-2)[/tex] and [tex](x,y) = (8/3,0)[/tex]
Here's my answer
hope it helps
The points (-6, r)
and
(6,3) lie on a line with slope 3/4. Find the missing coordinate r.
Answer:
r=-6
Step-by-step explanation:
[tex]m=\frac{y2-y1}{x2-x1} \\\frac{3-r}{6-(-6)} =\frac{3}{4} \\4(3-r)=3(12)\\12-4r=36\\-4r=24\\r=-6[/tex]
Select all of the statements that can be determined from the table given.
f(x)
Answer:
i don't know
Step-by-step explanation:
I don't know
Write the equation of the line that has a slope of 2 and passes through the point (-5, 1).
y = 2x - 5
y = 2x + 11
y = 2x + 1
y = 2x + 9
Step-by-step explanation:
= 2x +b
Use the given point (2, 5)
5 = 2(2) +b
b = 5 -4 = 1
The equation of the line is
y = 2x +1
Note general form of the slope-intercept form of a line is y = mx +b, where m is the slope and b is the y-axis intercept
Factorizie completely 2ap+aq-bq-2bp
Answer:
2ap + aq - bq -2bp = (a - b)(2p + q)
Step-by-step explanation:
(2ap + aq) - (bq -2bp)
a(2p +q) -b(q + 2p) [ taking a common from the first, and b from the second]
(2p + q) [a - b] [takin (2p + q)]
(2p + q)(a - b)
The completely factored form of the expression 2ap + aq - bq - 2bp is
(a - b)(2p + q).
In order to completely factorize the given expression, we need to look for common factors and apply factorization techniques.
Given expression: 2ap + aq - bq - 2bp
Step 1: Look for common factors.
Notice that 'a' is common in the first two terms, and '-b' is common in the last two terms.
Step 2: Factor out the common terms.
We can factor 'a' from the first two terms: a(2p + q)
And factor '-b' from the last two terms: -b(q + 2p)
Step 3: Rearrange the expression.
Now we have: a(2p + q) - b(q + 2p)
Step 4: Factor by grouping.
We can see that (2p + q) is common in both terms, so we can factor it out: (2p + q)(a - b)
Step 5: Final result.
Thus, the completely factored form of the given expression is
(a - b)(2p + q).
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The points plotted below are on the graph of a polynomial. Some of the roots to this polynomial are integers. Which of the following x-values are roots of the polynomial? Check all that apply.
Answer:
I think its B but I have very little evidence. Don't even put B but I was just saying I think it is.
Step-by-step explanation:
F(x) = -5x-3
G(x) = 4X^2 -3
Find f(3) and g(5)
Can you help me with these 3 !!!!!! And explain tooo!!!
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Answer:
See the attachment. Brainly doesn't like function constructs using f as a function name. Hence the picture.
Helppppp ASAPPPPPP TST FULL CREDIT
Answer:
24.
[tex] log_{2}(9) \\ = log_{2}(3) {}^{2} \\ = 3 log_{2}(3) \\ = \frac{3 log(3) }{ log(2) } \\ = 4.75[/tex]
25.
[tex]5. {9}^{x} = 12.48 \\ {9}^{x} = 2.496 \\ x log(9) = log(2.496) \\ x = \frac{ log(2.496) }{ log(9) } \\ x = 0.42[/tex]
26.
[tex]4 + 9. ln(x) = 15.8 \\ ln(x) = \frac{15.8 - 4}{9} \\ ln(x) = 1.311 \\ x = e {}^{1.311} \\ x = 3.71[/tex]
x < -5
f(x) =
(x + 6)2 +3 for
0
for
- 2x - 8
for
x = -5
X > -5
Find f(-7)
A bag contains exactly 50 coins. The coins are either worth 10 cents, 20 cents or 50 cents and there is Atleast one of each. The total value of the coins is $10. How many different ways can this occur?
Answer:
This can happen in two ways:
1) 42 20-cent coins, 6 10-cent coins and 2 50-cent coins.
2) 30 10-cent coins, 10 20-cent coins and 10 50-cent coins.
Step-by-step explanation:
Given that a bag contains exactly 50 coins, and the coins are either worth 10 cents, 20 cents or 50 cents and there is at least one of each, and the total value of the coins is $ 10, to determine how many different ways can this occur, the following calculation must be performed:
48 x 0.5 + 1 x 0.2 + 1 x 0.1 = 24.30
48 x 0.1 + 1 x 0.2 + 1 x 0.5 = 5.5
48 x 0.2 + 1 x 0.1 + 1 x 0.5 = 10.3
45 x 0.2 + 4 x 0.1 + 1 x 0.5 = 9.9
44 x 0.2 + 5 x 0.1 + 1 x 0.5 = 9.8
42 x 0.2 + 6 x 0.1 + 2 x 0.5 = 10
30 x 0.1 + 10 x 0.2 + 10 x 0.5 = 10
Therefore, this can happen in two ways:
1) 42 20-cent coins, 6 10-cent coins and 2 50-cent coins.
2) 30 10-cent coins, 10 20-cent coins and 10 50-cent coins.
Solve the equation by completing the square. X^2+10x+24=0
Answer:
x = -4
x = -6
Step-by-step explanation:
X^2+10x+24=0
(b/2)^2 = (10/2)^2 = 25
X^2+10x+25=-24+25
(x+5)^2 = 1
(x+5) = ± 1
x = +1 -5 = -4
x = -1 -5 = -6
This graph shows the amount of money Leo earns from tutoring compared with the number of hours he works. Select the correct statement about the graph.
A. For each hour he works, his earnings go up by $7.
B. For each hour he works, his earnings go up by $14.
C. For every 7 hours he works, his earnings go up by $1.
D. For each dollar he earns, the number of hours he works goes up by 14.
Answer:
B. For each hour he works, his earnings go up by $14.
Step-by-step explanation:
Given
The attached graph
Required
The true statement
The attached graph is a linear graph.
From the graph, we have:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (1,14)[/tex]
The rate (m) is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{14-0}{1-0}[/tex]
[tex]m = \frac{14}{1}[/tex]
[tex]m = 14[/tex]
This implies that the hourly rate is $14/hr
Hence (b) is true
the sum of two numbers is 20 one number is four less than the other. find the number
Answer:
is it 4 and 12 ?
Step-by-step explanation:
please let me know if it is correct! but i am 96% sure for me answer!
If the Circumstance of wobble ball is 242cm what is the surface area?
Answer:
1,166 is the SA
correct me if im wrong somehow
Step-by-step explanation:
a wobble ball is a sphere
circumference=8(pi)
242=8(3.14)
so 242 divided by 25.12
this ends up with 9.633757961783439, which is the radius of the circumference
SA of a sphere= 4(pi)r²
SA=4(3.14)9.633757961783439²
SA=4(3.14)92.80929246622581
SA=1,165.684713375796
rounded to the nearest whole # = 1166
Water runs from a faucet into a bucket at a steady rate. After 4 seconds, there are 32 ounces of water in the bucket. Write an equation that shows the relationship between time and ounces of water. Use t for time in seconds and w for ounces of water.
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Answer:
w = 8t
Step-by-step explanation:
If we assume that the ounces of water are proportional to the time, then the equation will look like ...
w = kt
for some constant k.
Solving for k, we find ...
k = w/t
Using the given values, we find k to be ...
k = (32 ounces)/(4 seconds) = 8 ounces/second
The units are stated in the definitions of the variables, so we can write the equation as ...
w = 8t
Which of the following is a point-slope equation of a line that passes through the points (-1, 4) and (8,-2)?
A. y-4= -3/2(x+1)
B. y-4= -2/3(x+1)
C. y-4= 2/3(x+1)
D. y-4= -2/3(x-1)
Answer:
B
Step-by-step explanation:
We want to find the point-slope equation of a line that passes through the points (-1, 4) and (8, -2).
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's find the slope of the line first. We can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{-2-4}{8-(-1)}=\frac{-6}{9}=-\frac{2}{3}[/tex]
We can choose (-1, 4) as our point. So, (x₁, y₁) = (-1, 4).
Substitute:
[tex]\displaystyle y-(4)=-\frac{2}{3}(x-(-1))[/tex]
Simplify:
[tex]\displaystyle y-4=-\frac{2}{3}(x+1)[/tex]
Therefore, our answer is B.
What is the completely factored form of this polynomial? 4x^4+12x^2+9
Answer:
(2x^2+3)^2
Step-by-step explanation:
See image below:)
Find the 7th term of the sequence
1, 4, 16, 64,...
28
16,384
4096
2401
Answer:
3rd option, 4096
Step-by-step explanation:
4⁰ = 1, 1st term
4¹ = 4, 2nd term
4² = 16, 3rd term
.
.
.
4⁶ = 4096, 7th term
Answered by GAUTHMATH
A culture started with 5,000 bacteria. After 4
hours, it grew to 5,500 bacteria. Predict how
many bacteria will be present after 13 hours.
Round your answer to the nearest whole
number.
P = Aekt
Answer:
5000 * (e^((1 /4) * ln(55 / 50) * (13))) = 6,815.47
Step-by-step explanation:
SOLVE ASAP! PLS HELP ME!!!
9514 1404 393
Answer:
A. 2.1
Step-by-step explanation:
Put the numbers in the equation and do the arithmetic.
1/R = 1/(3 1/2) +1/(5 1/4)
1/R = 1/(7/2) +1/(21/4) = 2/7 +4/21 = (6 +4)/21
R = 1/(10/21) = 21/10
R = 2.1
This graph represents a quadratic function. What is the function's equation written in factored form and in vertex form?
(graph in picture)
Step-by-step explanation:
f(x) = a(x-x1) (x-x2)
from the vertex, we get a:
0 = a(4-2)²- 8
4a = 8
a = 2
so, the equation:
f(x) = 2(x-0) (x-4)
f(x) = 2x(x-4)
f(x) = 2x² -8x
Arrange the steps to solve this system of linear equations in the correct sequence x+y=-2 2x-3y=-9
there you go the correct ans
Which equation is a linear function?
y=-5
y= 22 +7
y=22 - 1
y= ? +3
Answer:
let ? be x
every linear equation is y=mx+c
so the answer would be y=?+3
For the following right triangle, find the side length x . Round your answer to the nearest hundredth.
[tex]\huge\bold{Given:}[/tex]
Length of the base = 9
Length of the hypotenuse = 16 [tex]\huge\bold{To\:find:}[/tex]
✎ The length of the perpendicular ''[tex]x[/tex]".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
The length of the perpendicular [tex]x[/tex] is[tex]\boxed{±13.229}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ ⇢ {x}^{2} + {(9})^{2} = ({16})^{2} \\ ⇢ {x}^{2} + 81 = 256 \\ ⇢ {x}^{2} = 256 - 81 \\ ⇢x = \sqrt{175} \\ ⇢x = ±13.229[/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:perpendicular \:"x"\:is\:±13.229.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex]( {13.229})^{2} + ({9})^{2} = ({16})^{2} \\ ⇢ 175 + 81 = 256 \\ ⇢ 256 = 256 \\⇢ L.H.S.=R. H. S[/tex]
Hence verified. ✔
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]