We are told that the maximum amount to spend is $80 and that there is a 7.5% sales tax. If N is the amount we are going to spend then we need to have into account that we need to add the 7.5% of N and that should be at least equal to $80.
[tex]N+\frac{7.5}{100}N=80[/tex]Now we need to solve for N, to do that we add like terms:
[tex]\begin{gathered} (1+\frac{7.5}{100})N=80 \\ \frac{107.5}{100}N=80 \end{gathered}[/tex]Now we multiply both sides by 100:
[tex]107.5N=8000[/tex]Now we divide by 107.5:
[tex]N=\frac{8000}{107.5}[/tex]Solving the operations:
[tex]N=74.4\cong74[/tex]Therefore, the maximum amount to spend is $74
I know this is easy and i should know but im actually stumped on this one
For the given triangles:
There are 3 pairs of congruent angles
the triangles can not be proved using the congruent angles
the congruent angles used to prove the similarity of the triangles
So, the answer will be:
For the given triangle, we can not prove they are congruent.
Really need help solving this practice from my ACT prep guide It’s a trig practice
Given:
- The amplitude of the Sine Function:
[tex]A=10[/tex]- The midline:
[tex]y=4[/tex]- And the period:
[tex]Period=2[/tex]- You know that the function does not have a Phase shift.
• You need to remember that, by definition, the General Equation for a Sine Function has this form:
[tex]y=Asin\mleft(B\mleft(x+C\mright)\mright)+D[/tex]Where "A" is the amplitude, "C" is the phase shift, "D" is the vertical shift and this is the period:
[tex]Period=\frac{2\pi}{B}[/tex]Since the midline is given by the vertical shift, you can identify that, in this case:
[tex]D=4[/tex]And, knowing the period, you can set up that:
[tex]2=\frac{2\pi}{B}[/tex]Solving for "B", you get:
[tex]\begin{gathered} 2B=2\pi \\ \\ B=\frac{2\pi}{2} \\ \\ B=\pi \end{gathered}[/tex]• It is important to remember the following Transformation Rule for Functions:
When:
[tex]-f(x)[/tex]The function is reflected over the x-axis.
Therefore, knowing all the data, you can set up this equation:
[tex]f(x)=-10\sin (\pi x)+4[/tex]Hence, the answer is: First option.
Given the kite ABCD, which statement is false?Just the answer.
Explanation
let's check every option
then
A)
[tex]\angle ADC\text{ is congruente to }\angle ABC[/tex]we can see those angles (in black), aand as the lengths of the sides are similar this angles are congruente,so
[tex]\begin{gathered} \angle ADC\text{ is congruent to }\angle ABC \\ \text{true} \end{gathered}[/tex]B)
[tex]undefined[/tex]What is the 15th term in the sequence using the given formula?
Solution:
The formula is given below as
[tex]c_n=3n-1[/tex]Concept:
To figure out the 15th term, we will substitute n=15
By substituting values, we will have
[tex]\begin{gathered} c_{n}=3n-1 \\ c_{15}=3(15)-1 \\ c_{15}=45-1 \\ c_{15}=44 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow44[/tex]The THIRD OPTION is the right answer
If 2 dogs cross over a road and 1 dog disappear in the road how did the other dog made it
Answer:
he was quick???
Step-by-step explanation:
Mark me brainliest!
the parent function name for y=|x|
This function is an absolute type of function
Larry answered 8 out of every 10 questions correctly. The test had 70 questions. How many correct answers did Larry give?---What represents the "x" or unknown in this problem?
Representation of fractional numbers
Larry's rate of succesful questions is 8/10.
Then must find how many times is divided 70 in 10 questions
70/10 = 7
if there were a 100% succesful then 70 rresulted
but the rate is 8/10 , then multiply 8x 7 = 56 succesful questions for Larry.
what is the equation of a line that passes through point (-1,5) and has the slope of m=4
The general equation of a line is given as;
[tex]y=mx+b[/tex]In this question, the slope (which is m) is given as 4. Also we have the points x and y, given as (-1, 5). That is;
[tex]x=-1,y=5[/tex]Therefore the next step is to find the y-intercept (that is b in the equation).
We substitute for the known values as follows;
[tex]\begin{gathered} y=mx+b \\ 5=4(-1)+b \\ 5=-4+b \\ \text{Add 4 to both sides} \\ 5+4=-4+4+b \\ 9=b \end{gathered}[/tex]Now we know the value of b and m, we can substitute them as follows;
[tex]\begin{gathered} y=mx+b \\ m=4,b=9 \\ y=4x+9 \end{gathered}[/tex]Take away 5 from p????????????????
Answer:
p - 5
Step-by-step explanation:
5 - p = p - 5
Simplify f(x) = 2x^5 for x = 0, 1, 3, 5
f(0) = 0, f(1) = 2, f(3) = 486, f(5) = 6250
Explanations:The given function is:
[tex]f(x)=2x^5[/tex]To get the value of f(x) for x = 0, 1, 3, and 5, it means we are going to find f(0), f(1), f(3), and f(5).
[tex]\begin{gathered} f(0)=2(0)^5 \\ f(0)\text{ = 2(0)} \\ f(0)\text{ = 0} \end{gathered}[/tex][tex]\begin{gathered} f(1)=2(1)^5 \\ f(1)\text{ = 2(1)} \\ f(1)\text{ = 2} \end{gathered}[/tex][tex]\begin{gathered} f(3)=2(3)^5 \\ f(3)\text{ = 2 (}243) \\ f(3)\text{ = 486} \end{gathered}[/tex][tex]\begin{gathered} f(5)=2(5)^5 \\ f(5)\text{ = 2(}3125) \\ f(5)\text{ = }6250 \end{gathered}[/tex]What is the solution to 2x + 2(x – 5)=6,explainhow you solved the equation.explain with words
Answer
The solution to the equation is x = 4.
Explanation
We are told to find the solution to the equation
2x + 2(x - 5) = 6
The first step is to open the bracket by multiplying through by the number outside the bracket, that is, 2.
2x + 2x - 10 = 6
4x - 10 = 6
Add 10 to both sides to leave only 4x on the Left Hand Side.
4x - 10 + 10 = 6 + 10
4x = 16
Divide both sides by 4 to obtain the value of x.
(4x/4) = (16/4)
x = 4
Hope this Helps!!!
5) Francisco practiced playing his violin for 2 1/3 hours on Sunday. He practiced for 5/6 hour on Monday. How much time did Francisco spend playing his violin?(C)1 hours 3 (A)1 hours (B) hour (D) 3-hours, 10 min
Answer:
D
Francisco spent 3 hours, 10 minutes playing his violin
Explanation:
Given that:
Francisco practised playing his violin for
2 hours on Sunday
5/6 hours on Monday
The total number of time he spends playing his violin is obtained by adding the number of hours he spends each day.
[tex]\begin{gathered} 2\frac{1}{3}+\frac{5}{6} \\ \\ =\frac{7}{3}+\frac{5}{6} \\ \\ =\frac{19}{6} \\ \\ =3\text{ }\frac{1}{6} \end{gathered}[/tex]This is 3 hours, 10 minutes.
what is the range of the function graphed below?[tex]1 \leqslant y \ \textless \ 4 \\ - 3 \ \textless \ y \leqslant 3 \\ - 2 \leqslant y \leqslant 3 \\ - 3 \leqslant y \ \textless \ 4[/tex]
The range of the function is (-3, 3]
The range of a function is composed by all the values that y reaches in the function. Here we can see that the functions goes from 3 to -3. Then the range set is (-3, 3]. It has a parentheses in -3 because the function doesn't reach -3
10x2+4x factor completely
Answer:
2x * ( 5x + 2 )
Step-by-step explanation:
10x^2 = 2x * 5x
4x = 2x * 2
10x^2 + 4x = 2x * ( 5x + 2 )
Find the indicated probability. Round your answer to 6 decimal places when necessary.Find the probability of tossing 1 tails or 1 head on the first 8 tosses of a "fair" coin.
First, find the probability of getting 1 head in 8 tosses
P(1 head) = tosses with exactly 1 head/ total number of possible outcomes
number of outcomes = 2^8 = 256
number of outcomes with 1 head = 8 ( we could get 1 head on the first toss or on the second or on the third......)
P (1 head) = 8/256 = 1/32
The same would be true for tails
P(1 tail) = tosses with exactly 1 tail/ total number of possible outcomes
= 8/256 = 1/32
The formula to calculate the “or” probability of two events A and B is this: P(A OR B) = P(A) + P(B) – P(A AND B).
Since we cannot get P(1 head and 1 tail) since we toss 8 times
P (1head or 1 tail) = 1/32 + 1/32 = 2/32 = 1/16 =.0625
Select all the pairs that represent alternate interior angles.See image for instruction
Alternate means on the opposite side of the transversal, or line n
interior means inside of the parallel lines l and m
The alternate interior angles are 4 and 5
and 3 and 8
Check the boxes for both pairs
If the sum of a number and nine is tripled , the result is two less than twice the number. Find the number.
By solving a simple linear equation we will see that the number is -29.
How to find the number?Let's define x as the number, then the sentence:
"If the sum of a number and nine is tripled , the result is two less than twice the number"
Can be written as the equation:
3*(x + 9) = 2x - 2
This is a linear equation that we can solve for x:
3*(x + 9) = 2x - 2
3x + 27 = 2x - 2
3x - 2x = -2 - 27
x = -29
The number is -29.
Learn more about linear equations:
https://brainly.com/question/1884491
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May I please get help with this math problem please I have tried so many times but still could not get the right answers
We know that the sum of interior angles of a triangle equals 180, then, in this case we have the following:
[tex]90+2x+17+3x+28=180[/tex]solving for x, we get:
[tex]\begin{gathered} 90+2x+17+3x+28=180 \\ \Rightarrow135+5x=180 \\ \Rightarrow5x=180-135=45 \\ \Rightarrow x=\frac{45}{5}=9 \\ x=9 \end{gathered}[/tex]therefore, x = 9
Find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. When typing the point (x,y) be sure to include parentheses and a comma between your x and y components. Do not put any spaces between your characters. If a value is not an integer type your answer rounded to the nearest hundredth.3x+8y=24the x-intercept is Answerthe y-intercept is Answer
We want to find the x and y-intercepts of
[tex]3x+8y=24[/tex]The x-intercept is where the graph cuts the x-axis, when y = 0. To find this in our equation, we just need to evaluate it at y = 0.
[tex]\begin{gathered} 3x+8\times0=24 \\ 3x=24 \\ x=\frac{24}{3}=8 \end{gathered}[/tex]Then, the x-intercept is (8, 0).
The y-intercept is where the graph cuts the y-axis, when x = 0. To find this in our equation, we just need to evaluate it at x = 0.
[tex]\begin{gathered} 3\times0+8y=24 \\ 8y=24 \\ y=\frac{24}{8}=3 \end{gathered}[/tex]The y-intercept is (0, 3).
What is the surface area of the solid that this net can form?8 mm25 mm8 mm5 mm5 mm8 mm8 mm5 mm5 mm8 mm8 mm25 mmO 730 square millimetersO 875 square millimeters0 1,000 square millimetersO 1,444 square millimeters
The solid is formed by 6 rectangles.
Calculate the area of each one and then add them to obtain the surface area (SA),
Area of a rectangle: Length x width
A1 = 8 x 5 = 40 mm2
A2= 25x5 = 125 mm2
A3 = 8 x 5= 40 mm2
A4 = 25 x 8 = 200 mm2
A5 = 25x5 = 125 mm2
A6 = 25 x 8 = 200mm2
SA = A1+A2+A3+A4+A5+A6 = 40 + 125 +40 +200 +125+ 200 = 730 mm2
6. Cesium-137 has a half-life of 30 years. Suppose a lab stores 30 mg in 1975. How much would be left in 2065? y = a (1 + r) (Fill in answer choices for a, r and t.)
The formula for calculating the amount remaining after a number of half years , n is :
[tex]\begin{gathered} A=\frac{A_{\circ}}{2^n^{}} \\ \text{where A}_{\circ}\text{ =initial }amount \\ n=\frac{t}{t_{\frac{1}{2}}} \end{gathered}[/tex]The lab store mass of Cesium-137 is 30mg in 1975
then the mass of Cesium-137 in 2065,
Time period =2065-1975
time period t=90 years,
substitute the value and solve for A
[tex]\begin{gathered} A=\frac{30}{2^{\frac{90}{45}}} \\ A=\frac{30}{2^2} \\ A=\frac{30}{4} \\ A=7.5\text{ mg} \end{gathered}[/tex]In 2065, the mass of Cesium -137 will be 7.5 mg
Answer : 7.5mg
can someone please help me solve and graph this the past few have been incorrect and this is my homework and i really need help
step 1
Solve the inequality
[tex]\begin{gathered} 3x+8\leq11 \\ 3x\leq11-8 \\ 3x\leq3 \\ x\leq1 \end{gathered}[/tex]the solution for the first inequality is the interval
(-infinite, 1]
step 2
Solve the inequality
[tex]\begin{gathered} 3x+8\text{ > 20} \\ 3x\text{ > 20-8} \\ 3x\text{ > 12} \\ x\text{ > 4} \end{gathered}[/tex]the solution for the second inequality is the interval
(4, infinite)
step 3
the general solution for the first inequality or the second inequality is
(-infinite, 1] U (4, infinite)see the attached figure to better understand the problemwhich of the following could be the combination of values for the students and the minimum numbers of chaperones the museum requires
3 chaperones ---------------------------- 24 students
9 chaperones --------------------------- 72 students
2chaprones 16 students
7.5 chaperones ----------------------- 60 students
5.6 chaperones------------------------ 45 students
5 chaperones ------------------------- 40
The first two options are correct
A state sales tax of 6% and a local sales tax of 1% are levied in Tampa, Florida. Suppose the price of a particular car in Tampa is $15,000, and an oil change at a certain auto center is $29.Which statement is true another total cost of the car and the oil change after sales tax has been calculated?Select the correct answer
We have the following:
What we must do is calculate the total cost of the car by adding its original value plus the cost of taxes, 6% and 1%
We know that the initial value is $15000, if to that we add 6% of those $15000 and equal 1%, we have
[tex]15000+15000\cdot0.06+15000\cdot0.1=15000+900+150=16050[/tex]We do the same procedure for the oil change
[tex]29+29\cdot0.06+29\cdot0.01=29+1.74+0.29=31.03[/tex]Therefore the correct statement is the last
I need help on this equation. It’s algebra. SAT PREP.
Answer:
r = 1.14
Explanation:
The value of a product (A) over time with an increasing rate "i" can be calculated as follows:
A = C(1+i)^t
where:
C is the value of the product at time 0;
A is the value of the product at time t;
i is the increasing rate.
If we compare the expression V=300r^t with A = C(1+i)^t. We can observe that:
r = 1+i
r = 1+0.14
r = 1.14
7(-a-3)=3(2a-6) I have the answer but I need help checking it.
SOLUTION:
Step 1:
In this question, we are meant to solve the following:
[tex]7\text{ ( - a - 3 ) = 3 ( 2a - 6 )}[/tex]Step 2:
Simplifying, we have that:
[tex]\begin{gathered} -7a\text{ - 21 = 6a - 18} \\ \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} -21\text{ + 18 = 6 a + 7a} \\ 13\text{ a = -3} \\ \text{Divide both sides by 13, we have that:} \\ a\text{ = }\frac{-3}{13} \end{gathered}[/tex]Step 3:
To verify that:
[tex]a\text{ =}\frac{-3}{13}[/tex]is a solution, we have that:
[tex]7\text{ ( - a - 3 ) = 7 \lbrack -(}\frac{-3}{13}\text{ ) - 3 \rbrack}[/tex][tex]7\lbrack\text{ }\frac{3}{13}\text{ - 3\rbrack = 7 \lbrack }\frac{3}{13}\text{ - }\frac{39}{13}\text{ \rbrack = 7 x }\frac{-36}{13}\text{ = }\frac{-252}{13}\text{ ( Left Hand Side)}[/tex]Next,
[tex]3\text{ ( 2 a - 6 ) = 3 \lbrack{}2(}\frac{-3}{13})\text{ - 6 }\rbrack\text{ = 3 \lbrack}\frac{-6}{13}\text{ - 6\rbrack= 3\lbrack}\frac{-6}{13}\text{ - }\frac{78}{13}\rbrack[/tex][tex]=\text{ 3 \lbrack }\frac{-84}{13}\text{ \rbrack = }\frac{-252}{13}\text{ ( Right Hand Side)}[/tex]CONCLUSION:
From the solution and from the verification of the answers, we can see that the correct answer is:
[tex]a\text{ = }\frac{-\text{ 3}}{13}[/tex]1f(x) =X-24g(x)ХFind: (fog)(x) =
We have the functions:
[tex]undefined[/tex]s
How many different regrestation codes are possible. And also what is the probability that all the first three digits of the code are not even numbers.
a) Consider the 7-digit registration code to be an arrangement of 7 cells to be filled using the given digits.
In the first cell, one can write any of the digits; on the other hand, there are only 6 digits available to fill the second cell (no number can be used more than once). Therefore, there are 5 digits that can be used in the third cell and so on; thus, there is a total of
[tex]7*6*5*4*3*2*1=7!=5040[/tex]5040 different registration codes.b) The 5040 different combinations found above are equally probable.
There are only 3 available even numbers (2, 4, and 6); therefore, we need to find the number of combinations such that none of the first three digits is equal to 2, 4, or, 6.
Thus, using a diagram,
There are 4 possible numbers that one can fit in the first cell (1,5,7, or 9), in the second cell, one can fit 3 numbers (any of the remaining ones from cell 1), and so on.
In the fourth cell (first cell in blue), one can fit any even number plus a remaining odd number from cell 3.
Therefore, the total number of codes such that their first three digits are not even are
[tex]4*3*2*4*3*2*1=576[/tex]Then, the corresponding probability is
[tex]P=\frac{576}{5040}=\frac{4}{35}[/tex]The answer to part b) is 4/35For the problem below, find the reference angle, to the nearest 10th (if necessary), and also the two possible quadrants in which θ could lie.tan(θ)=−3
The two possible quadrants are the second and the fourth
8. MOVIE TICKETS Tickets to a movie cost $25 for adults and 5.50 formodents A group of friends purchased 8 tickets for $52.75 a Write a system of equations to represent the station
Tickets for adults --> $25
Tickets for formodents --> $5.50
The equations that would represent the number of adults and formodents in th group of friends:
Let x be adults
Let y be formodents
$25x+$5.50y=$52.72
x+y=8