In order to calculate the sales tax to 45, calculate the 9% of 45, just as follow:
(9/100)(45) = 4.05
Hence, the sales tax is $4.05
151617= 1819Write an equation in slope-intercept form for the line with slope 5 and y-intercept - 1.00=0:Х?
The slope-intercept format of a line is given as y=mx+c where m is the slope and c is the intercept.
Since m=5 and c=-1
Therefore the equation of the line is y = 5x-1
Two step equations 0=4+n/5
SOLUTION
We want to solve the equation
[tex]0=4+\frac{n}{5}[/tex]This means we should solve for n or find n. This becomes
[tex]\begin{gathered} 0=4+\frac{n}{5} \\ \text{moving 4 to the other side of the equation, we have } \\ -4=\frac{n}{5} \\ \text{Hence } \\ \frac{n}{5}=-4 \\ m\text{ultiplying both sides of the equation by 5, we have } \\ \frac{n}{5}\times\frac{5}{1}=-4\times5 \\ n=-20 \end{gathered}[/tex]Hence, the answer is n = -20
V8 to the nearest tenth is about ?
8 1/3% Convert each percent to a fraction and a decimal.
We must convert the percentage 8 1/3% to:
0. a fraction,
,1. a decimal.
First, we rewrite the number 8 1/3 in the following way:
[tex]8\text{ 1/3 }=8+\frac{1}{3}=8\cdot1+\frac{1}{3}=8\cdot\frac{3}{3}+\frac{1}{3}=\frac{8\cdot3+1}{3}=\frac{25}{3}\text{.}[/tex]Now, we have that:
[tex]8\text{ 1/3 \% }=\frac{25}{3}\text{ \%.}[/tex]1) Because 8 1/3 % is 8 1/3 per 100, we have that:
[tex]8\frac{1}{3}％=\frac{8\frac{1}{3}}{100}=\frac{\frac{25}{3}}{100}=\frac{25}{3\cdot100}=\frac{25}{3\cdot4\cdot25}=\frac{1}{12}\text{.}[/tex]2) Using a calculator, we have:
[tex]8\frac{1}{3}％=\frac{1}{12}\cong0.083.[/tex]Answer
• 8 1/3% as a ,fraction, is ,1/12,,
,• 8 1/3% as a ,decimal, is ,0.083,.
To support the high school, the local businesses will donate $2 for every ticketsold at the homecoming game. If 113 student, 158 home and 52 visitor ticketswere sold, how much did they donate?
we know that
to find out the total amout donate, multiply the total tickets sold by $2
so
step 1
Find the total tickets sold
adds
113+
Determine if the triangles are similar; if they are then what is the reason?
From the given triangles,
[tex]\frac{OP}{PN}=\frac{RS}{SQ}[/tex][tex]\angle OPN=\angle RSQ=89^O[/tex]Thus the triangles are similar by SAS property.
The relation is SAS: two sides+included angle congruent.
for every dollar of revenue the government takes in, it pays 5 cents in interest on its debtwhat is the ratio of debt interest to total revenue a. 1:4b. 1:5c. 1:10d. 1:20
Answer;
D. 1:20
Explanation
According to the question, we are given the following
Total revenue = 1 dollars
Debt interest = 5cents
Ratio of debt interest to total revenue = 5cents : 1 dollar
Since 1 dollar = 100cents
ratio of debt interest to total revenue = 5cents : 100cents
ratio of debt interest to total revenue = 5/100 = 1/20
Hence the ratio of debt interest to total revenue is 1:20
At the Avonlea Country Club, 54% of the members play bridge and swim, and 89% of the members play bridge. If a member is selected at random, what is the probability that the members swims, given that the member plays bridge?
ANSWER
[tex]P(S|B)=0.61[/tex]EXPLANATION
We are given that 54% of the members at the club play bridge and swim, and 89% of the members play bridge.
[tex]\begin{gathered} P(\text{BnS)}=0.54 \\ P(B)=0.89 \end{gathered}[/tex]To find the probability that the member swims given that he/she plays bridge, we have to apply conditional probability.
The probability that the member swims given that he/she plays bridge is gotten by dividing the probability that the member plays bridge and swims by the probability that the member plays bridge:
[tex]\begin{gathered} P(S|B)=\frac{P(B\cap S)}{P(B)} \\ \Rightarrow P(S|B)=\frac{0.54}{0.89} \\ P(S|B)=0.61 \end{gathered}[/tex]That is the answer.
evaluate. Reduce your answer to lowest terms.2 1/5-10×(3/5)2
reduce the radical of 200
Neil and Tom love to collect baseball cards. Neil has 83 more baseball cards than Tom. Neil has 517 baseball cards,How many baseball cards does Tom have?
We start by labeling the number of cards of each. The number of cards that Neil has will be "N", and the number of cards that Tom has will be "T".
We are told that Neil has 83 more baseball cards than Tom, this can be represented in an equation:
[tex]N=T+83[/tex]In this expression, we say that the number of cards that Neil has is equal to the number of cards that Tom has plus 83 more cards.
Since the problem also indicates that Neil has 517 baseball cards:
[tex]N=517[/tex]And we can combine the two equations we have as follows:
[tex]T+83=517[/tex]With this last equation, we will be able to find the number of baseball cards that Tom has, by solving for T.
To solve for T, we subtract 83 to both sides of the equation:
[tex]T+83-83=517-83[/tex]On the left side +83-83 cancel each other:
[tex]T=517-83[/tex]And making the subtraction on the right side, we get the value of T:
[tex]T=434[/tex]Tom has 434 baseball cards.
Answer: 434
Solve for a.2(a+4)+6a=48 Enter your answer in the box.a =
Step 1
Given
[tex]2(a+4)+6a=48[/tex]Required : To find the value of a
Step 2
Expand the bracket
[tex]2a+8+6a=48[/tex]Step 3
Bring like terms together
[tex]\begin{gathered} 2a+6a=48-8 \\ \end{gathered}[/tex]Step 4
Find the value of a
[tex]\begin{gathered} 8a\text{ = 40} \\ \frac{8a}{8}=\frac{40}{8} \\ a=\text{ 5} \end{gathered}[/tex]Hence, a = 5
Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again.(a) What is the probability that the second roll is also a "4".P(4 | 4) =(b) What is the probability that the second roll is a "1".P(14)
The outcome of the second roll is independent from the previous outcome. The probability of getting any given number from 1 to 6 is always the same: 1/6.
Therefore, the answers are:
a) The probability that the second roll is also a 4 is 1/6.
b) The probability that the second roll is a 1 is 1/6.
Find the slope of a line a. parallel and b. perpendicular to the line y = - 3x + 8.a. Parallel:b. Perpendicular:
The slope of a line parallel to the given line is -3
The slope of the line perpendicular to the given line is 1/3
Explanation:
Given:
y = -3x + 8
To find:
a) slope of a line parallel to the given line
b) slope of a line perpendicular to the given line
a) For two lines to be parallel, their slopes will be the same
From the given equation, we will get the value of the slope
[tex]\begin{gathered} linear\text{ equation: y = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \\ \\ comparing\text{ y = mx + b with y = -3x + 8}: \\ mx\text{ = -3x} \\ m\text{ = -3} \end{gathered}[/tex]The slope of a line parallel to the given line is -3
b) For two lines to be perpendicular, the slope of one line will be the negative reciprocal of the other line
The slope from the line given is -3
reciprocal of the slope = 1/-3 = -1/3
negative reciprocal = -(-1/3) = 1/3
The slope of the line perpendicular to the given line is 1/3
Could you help walk me through this problem? I keep getting the problem wrong and I don't know why.
to solve this we can get the equation in the form
F(x)=a(x-X1)(x-X2)
where X1 and X2 are the values of X where the line cross the axial X
in this case
X1= -1
X2= 2
so the function will be
F(x)=a*(x+1)*(x-2)
now we need to find the value of a
So for this we can replace with a random point of the curve, for example the point x= 0 y=-2
So if we replace
-2=a*(0+1)*(0-2)
-2=a*1*-2
-2=a*-2
-2/-2=a=1
So the answer is:
F(x)=1*(x+1)*(x-2)
Combine Like Terms -8w + 16x + 20w – 40x
Answer:
12w - 24x
Step-by-step explanation:
-8w + 16x + 20w - 40x
20w - 8w = 12w
-40x + 16x = 24x
Answer:
12w - 24xStep-by-step explanation:
Start by grouping terms that are alike. You can identify such terms by looking at the variables. Anything associated with x is considered a like term to another number associated with x.[tex]-8w+16x+20w-40x\\-8w+20w+16x-40x[/tex]
Add both like elements for each side.[tex]-8w+20w=12w\\12w+16x-40x\\16x-40x=-24x\\\bold{=12w-24x}[/tex]
Hope this helps!
4312345L2-3445To find the rate of change of the function, Kevin did the following:
What is the slope of a linear function that passes between (2, 7) and (5, 12)?
The formula of slope,
→ (y2 - y1)/(x2 - x1)
Then the slope will be,
→ m = (12 - 7)/(5 - 2)
→ [ m = 5/3 ]
Hence, thy slope is 5/3.
Me podrían ayudar a contestar estas preguntas, por favorspeak spanish
En un parallelogramo, los lados opuestos son paralelos. De la misma forma, los angulos opuestos son iguales y los angulos adjacentes suman 180 grados.
Con ello, podemos decir que:
a. Los lados RS y UT son paralelos.
b. Los lados RU y ST son paralelos.
c. El angulo en U es igual al angulo en S pues son opuestos
d. Los angulos en S y T son adjacentes . Esto quiere decir que, su suma es igual a 180 grados.
e. El angulo en R es igual al angulo en T pues son opuestos.
f. De forma similar al caso d, los angulos U y R son adjacentes, su suma es 180 grados.
The graph below shows the cost for going roller skating at 2 roller rinks . Bianca is going roller skating with a group of friends . Roller Rink A charges $3.00 per person and a $60 group fee . Roller Rink B charges $7.00 per person and an $8.00 group fee . When comparing costs ,which statement is true ? • Roller Rink B always cost less • Roller Rink A always cost less • Roller Rink B costs less if Bianca's group has fewer then 13 people• Roller Rink A costs less if Bianca's group has fewer then 13 people
In this case we can see that the cost of each company is increasing but the slopes are diferent. also we can see that the cost of company B is is cheaper at the begining but after some peaple is more expensive so the correct statement will be:
Roller Rink B costs less if Bianca's group has fewer than 13 people
1. A taxi company charges an $8 fee for picking you up, plus an additional $1.75 for each mile that you travel. The last customer to use the company was charged 34.25 for their taxi ride. How many miles did they travel in the taxi?
they travelled 15 miles
Explanation:let the number of miles = m
The total charge per ride= $8 + (amount for each mile × number of miles)
amount for each mile = $1.75
The total charge = $8 + ($1.75 × m)
The total charge per ride = 8 + 1.75m
Last customer paid $34.25
34.25 = 8 + 1.75m
collect like terms:
34.25 - 8 = 1.75m
26.25 = 1.75m
divide both sides by 1.75:
26.25/1.75 = 1.75m/1.75
m = 15
Hence, they travelled 15 miles
The volume V of a cone varies jointly as the square of the radius of the base,r, and the height, h. Find the equation of the joint variation if v =285, r=4, and h = 17.
Answer:
V = 1.05r²h
Explanation:
The expression ''the volume V of a cone varies jointly as the square of the radius of the base,r, and the height, h'' can be represented as:
[tex]V=k\cdot r^2\cdot h[/tex]Where the k is a constant.
So, replacing V = 285, r = 4, and h = 17, we get:
[tex]285=k\cdot4^2\cdot17[/tex]Solving for k, we get:
[tex]\begin{gathered} 285=k\cdot16\cdot17 \\ 285=k\cdot272 \\ \frac{285}{272}=\frac{k\cdot272}{272} \\ 1.05=k \end{gathered}[/tex]So, the equation of the joint variation is:
[tex]V=1.05r^2h[/tex]The Washington Monument, in Washington, D.C., is 555 feet 5% inches tall and weighs 90,854 tons. The monument is topped by a square aluminum pyramid. The sides of the pyramid's base measure 5.6 inches, and the pyramid is 8.9 inches tall. Estimate the slope that a face of the pyramid makes with its base. Round to the nearest tenth.
Sides of the pyramid are:
5.6 inches base
Height of the pyramid is:
8.9 inches
Let's recall the formula of the slope:
Slope = Change in y/Change in x
Let x = 8.9 or change in vertical distance
Let y = 2.8 or change in horizontal distance
Slope = 8.9/2.8
Slope = 3.1785
Slope = 3.2 rounding to the next tenth
21 The number of students in each of 2 exercise classes was the same. The box and whiskerplots below represent the average amount of time the students in each class spent exercisingdaily outside class.First class九术也Second class A+153012010545 6075 90Time Spent Exercising(minutes)Based on the information in the box and whisker plots, which statement about the time spentexercising outside class appears to be true?A The median amount of time the first class spent exercising was greater than the medianamount of time the second class spent exercising.B The range for the second class was less than the range for the first class.C The interquartile range for the first class was less than the interquartile range for thesecond class.D The minimum amount of time the second class spent exercising was greater than theminimum amount of time the first class spent exercising.
We are given a box and whiskers plot and we are asked the following questions:
A. The median amount of time the first class spent exercising was greater than the median amount of time the second class spent exercising.
The median of the first class is 60 and the median of the second class is 75, therefore, the median of the second class is greater than the median of the first class.
B. The range for the second class was less than the range for the first class.
The range of the first class is:
[tex]r_1=90-30=60[/tex]The range of the second class is:
[tex]r_2=105-30=75[/tex]Therefore, the rage of the second class is greater than the range of the first class.
C. The interquartile range for the first class was less than the interquartile range for the
second class.
The Interquartile range of the first class is:
[tex]IQ_1=75-45=30[/tex]The interquartile range of the second class is:
[tex]IQ_2=90-45=45[/tex]Therefore, the interquartile range of the first class is less than the interquartile range of the second class.
D The minimum amount of time the second class spent exercising was greater than the minimum amount of time the first class spent exercising.
The minimum time for the first class is 30 and the minimum time for the second class is 30, therefore, the minimum times are equal.
Write the polynomial in factored form as a product of linear factors:g(t)=t^3+2t^2−10t−8
Okay, here we have this:
We need to write the following polynomial in factored form as a product of linear factors:
[tex]\begin{gathered} g\mleft(t\mright)=t^3+2t^2-10t-8 \\ =\mleft(t+4\mright)\mleft(t^2-2t-2\mright) \end{gathered}[/tex]Now, let's solve the following polynomial using the general formula for equations of the second degree:
[tex]\begin{gathered} (t^2-2t-2)=0 \\ t_{1,\: 2}=\frac{-\left(-2\right)\pm\sqrt{\left(-2\right)^2-4\cdot\:1\cdot\left(-2\right)}}{2\cdot\:1} \\ t_{1,\: 2}=\frac{-\left(-2\right)\pm\:2\sqrt{3}}{2\cdot\:1} \\ t_1=\frac{-\left(-2\right)+2\sqrt{3}}{2\cdot\:1},\: t_2=\frac{-\left(-2\right)-2\sqrt{3}}{2\cdot\:1} \\ t=1+\sqrt{3},\: t=1-\sqrt{3} \end{gathered}[/tex]Finally, we obtain the following polynomial:
[tex]g(t)=(t+4)(t-1-\sqrt{3})(t-1+\sqrt{3})[/tex]Find the sum of the first 46 terms of the following series, to the nearestinteger.12, 15, 18, ...
We can see that this is an arithmetic sequence. The first term is 12 and the common difference is 3.
Using the formula to calculate the sum of the first 46 terms, we have:
[tex]undefined[/tex]Graph y < -1 in a coordinate plane. And Label the Axis
Answer:
Explanation:
Given the below inequality;
[tex]y<-1[/tex]To graph the above, we have to note that since we have the less than sign without an inequality sign, the line will be broken lines and we'll shade the downward part of the graph as shown below;
I just need the answer
The Solution.
The line of symmetry occurs at x= -2
And the maximum value of the given function is 8, and it occurs at x = -2
2221. Admission to a science museum is $22for an adult. The cost for a child is $5 lessthan the cost for an adult. What would bethe total cost of admission for 12 adultsand 15 children? Explain.
the cost for an adult admission is 22 $
cost for child is 22 - 5 = 17 $
total cost for 12 adults is 12 x 22 = 264
total cost for 15 children is 15 x 17 = 255
so the total cost of admission for 12 adults and 15 children is,
= 264 + 255
= 519 $
so the answer is 519 $
Determine the amount of an investment if $100 is invested at an interest rate of 5.5% compounded semi-annually for 6 years.
We have an investment that is compounded semi-anually.
The equation for the future value of an compounded interest investment is:
[tex]FV=PV(1+\frac{r}{m})^{n\cdot m}[/tex]where:
FV is the future value.
PV is the present or initial value of the investment (PV=100).
r is the annual nominal interest rate (r=5.5%=0.055).
m is the number of capitalization subperiods in the year. In this case, as it is semiannually, m=12/6=2.
n is the number of yearly periods that the investment last (n=6 years).
Then, we can replace the variables with the values and calculate:
[tex]\begin{gathered} FV=100\cdot(1+\frac{0.055}{2})^{2\cdot6} \\ FV=100\cdot(1+0.0275)^{12} \\ FV=100\cdot1.0275^{12} \\ FV\approx100\cdot1.3848 \\ FV\approx138.48 \end{gathered}[/tex]Answer: the value of the investment after 6 years is $138.48.