Solution
Miguel and 3 of his friends went to the movies.
They originally had a total of $40.00.
Since each boy have the same amount, let the amount each boy have left after the ticket be m
The amount each boy have left is
[tex]4\times m=4m[/tex]Each boy spent $7.50 on a ticket, i.e
[tex]4\times7.5[/tex]The amount of money that each boy have left can be expressed as
[tex]\begin{gathered} 4m+4(7.5)=40 \\ 4(m+7.5)=40 \end{gathered}[/tex]Solving for m
[tex]\begin{gathered} 4(m+7.5)=40 \\ \text{Divide both sides by 4} \\ \frac{4(m+7.5)}{4}=\frac{40}{4} \\ m+7.5=10 \\ \text{Collect like terms} \\ m=10-7.5 \\ m=\text{ \$2.5} \end{gathered}[/tex]Hence, each boy have $2.5 left after buying his ticket.
Answer: $2.50 would be your answer!
Step-by-step explanation: $7.50 x 4 = 30
40$ - 30 = 10
10 ÷ 4 = 2.50
hope this helps! :)
Function gis represented by the equation.g(x)=9(1/3)^x-4Which statement correctly compares the two functions?
So,
As you can see, the function g:
[tex]g(x)=9(\frac{1}{3})^x-4[/tex]Has the same behavior of the graph above.
That's because the rate (1/3) is less than 1, so the graph will decay.
The y- intercept of the function g is obtained when we make x=0:
[tex]\begin{gathered} g(0)=9(\frac{1}{3})^0-4 \\ g(0)=9-4 \\ g(0)=5 \end{gathered}[/tex]If we compare, both y-intercepts seem to be different.
Therefore,
Which expressions are equivalent to log_4 (1/4 x2)
Answer:
The expression equivalent to the given logarithm is:
[tex]2\log _4(\frac{x}{2})[/tex]Explanation:
We want to know which expressions are equivalent to
[tex]\log _4(\frac{1}{4}x^2)[/tex]We have:
[tex]\begin{gathered} \log _4(\frac{x}{2})^2 \\ \\ =2\log _4(\frac{x}{2}) \end{gathered}[/tex]Determine the most specific name for quadrilateral JKLM if the coordinates of the vertices are:J(-4,6), K(-1,2), L(1,6), M(4,2)JL ll KM PROOF:J.5JL is parallel to X-axis.bothvertices have y-coordinate at y = 6.KM Parallel to x axis, bothvertices have y-coordinate aty=2.43KM M1Determine Stopes of JK & LM(If slopes ave ithen sides arparallel):4517-42-8-3-10JK: 31-4,6) K(+1,2)x2 Y2xiyo2-6-4
To finish the demonstration that the quadrilateral JKLM is a rhombus we need to prove that side JK is congruent with side LM.
The length of a segment with endpoints (x1, y1) and (x2, y2) is calculated as follows:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting with points L(1,6) and M(4,2) we get:
[tex]\begin{gathered} LM=\sqrt[]{(4-1)^2+(2-6)^2} \\ LM=\sqrt[]{3^2+(-4)^2} \\ LM=\sqrt[]{9+16^{}} \\ LM=5 \end{gathered}[/tex]Given that opposite sides are parallel, all sides have the same length, and, from the diagram, the quadrilateral is not a square, we conclude that it is a rhombus.
Find the diameter of the circle.The image shows a circle with radius 9 centimeters.The diameter of the circle is _______ centimeters.The solution is _______
The diameter of the circle is given as
[tex]\begin{gathered} \text{diameter}=2\times radius\text{ of the circle} \\ d=2r \end{gathered}[/tex]The given radius is
[tex]=9\operatorname{cm}[/tex]Therefore, the diameter will be
[tex]\begin{gathered} \text{diameter =2}\times9\operatorname{cm} \\ \text{diameter =18cm} \end{gathered}[/tex]Hence,
The diameter of the circle =18 centimeters
Find the polynomial that represents the perimeter of the figure. simplify your answer.
The given diagram is a pentagon with different side measurements.
The perimeter is defined as the sum of all external boundaries of the figure.
So the perimeter (P) of the pentagon is equal to the sum of the 5 sides of the figure,
[tex]\begin{gathered} P=(3t^2-9)+(3t^2-9)+(2t^2+5)+(2t^2+5)+(t^3-t^2+8) \\ P=3t^2-9+3t^2-9+2t^2+5+2t^2+5+t^3-t^2+8 \\ P=t^3+(3t^2+3t^2+2t^2+2t^2-t^2)+(-9-9+5+5+8) \\ P=t^3+9t^2+(0) \\ P=t^3+9t^2 \end{gathered}[/tex]Thus, the perimeter of the figure is,
[tex]t^3+9t^2[/tex]AC, DF, and GI are parallel. Use the figure to complete the proportion.JFFE?DE
Given that AC, DF, and GI are parallel, we can see that line JH bisects angle J. This means that triangles formed with the parallel lines are similar. Considering triangle JDF,
JF corresponds to JD
FE corresponds to DE
Thus, the ratios are
JF/FE = JD/DE
Cecily's teacher held a raffle. To win the raffle, a student has to pick a paper scroll with an integer written on it. The chart shows the scrolls picked by Cecily and her friends. Name Paper Scroll Cecily 6.7 Marty -37 Jon 7/ 9 Fiona 3 1/3who picked the winning scroll a. Cecily picked the winning scrollb.Marty picked the winning Scrollc.jon picked the winning scrolld. fiona picked the winning scroll
Answer:
Note:
Integers are whole numbers.
They include 0, negative whole numbers, and positive whole numbers
Since the condition to win the rafle is to pick an interger, let us consider the number picked by each of the students and see if it is an integer or not.
Cecily picked 6.7
This is a decimal number, it is not an integer
Marty picked -37
This is an integer, since it is not a decimal and does not have a fraction component
Jon picked 7/9
This is a proper fraction, and it is not an integer
Fiona picked 3 1/3
This is a mixed fraction, it is not an integer.
The only student that picked an integer number is Marty, hence, she is the winner of the raffle.
Graph the function by first finding the relative extrema. f(x) = x² + 4x2-x-4 7 4 6 2
Graph the function by first finding the relative extrema.
__________________________________
f(x) = x^3 + 4x^2 - x - 4
f'(x) = 3x ^2 + 8x -1
c= 3x ^2 + 8x -1
Using the quadratic equation
[tex]x=\frac{-b\text{ }\pm\text{ }^{}\sqrt[]{b^2\text{ -4ac}}}{2a}\text{ = }\frac{-(8)\text{ }\pm\text{ }^{}\sqrt[]{8^2\text{ -4}\cdot3\cdot\text{ (-1)}}}{2\cdot3}[/tex]___________________
They want you to see the extreme points, but the easiest way is to evaluate 0 and check which graph matches
f(0) = 0^3 + 40^2 - 0 - 4
Point (0, -4)
85 is ___ tens and 25 ones
Answer:
6
Step-by-step explanation:
Because 25 ones is 25
So 85 - 25 = 60
60 = 6 tens
I need help graphing and I need to know the coordinates. The graph goes up to 12.
We have the next given function:
[tex]f(x)=\sqrt[3]{x}-2[/tex]To find the first point, we need to use:
[tex]\sqrt[3]{x}=0[/tex]Solve the equation for x:
[tex](\sqrt[3]{x})^3=(0)^3[/tex][tex]x=0[/tex]So, when x=0, we got the first point (0, -2), because:
[tex]y=\sqrt[3]{x}-2[/tex][tex]y=0-2[/tex]Then
[tex]y=-2[/tex]Let's find the points on right, let use x=8 and x=27
Replace on the function, when x=8
[tex]y=\sqrt[3]{x}-2[/tex][tex]y=\sqrt[3]{8}-2[/tex][tex]y=2-2[/tex][tex]y=0[/tex]So, it represents the point (8,0)
Now, when x=27
[tex]y=\sqrt[2]{27}-2[/tex][tex]y=3-2[/tex][tex]y=1[/tex]This corresponds to the point (27,1)
Now, for points on the left side:
When x=-8
[tex]y=\sqrt[3]{-8}-2[/tex][tex]y=-2-2=-4[/tex]Which represents the point (-8,-4)
When x=-27
[tex]y=\sqrt[3]{-27}-2[/tex][tex]y=-3-20-5[/tex]Which represents the point (-27, -5)
Finally, graph these four points on the cartesian plane.
Consider the fraction 1/2, if this fraction is divided by 3, will the quotient be more or less than the quotient in the first part?
The table shows values for a linear function, f(x). What is an equation for f(x)?
Given a table that shows values for a linear function, f(x). we are asked to determine the equation of f(x).
Table:
x f(x)
-1 -8
3 -5
7 2
11 1
First, let us consider the lines of the equation as:
f(x) = ax + b
When x = -1 f(x) = -8
f(-1) = a(-1) + b
-8 = -a + b ------------------ eqn I
When x = 3 f(x) = 5
f(3) = a(3) + b
-5 = 3a + b ------------------- eqn II
subtract eqn I from eqn II:
-5 - (-8) = (3a + b) - (-a + b)
-5 + 8 = 3a + b + a - b
3 = 4a (-b and +b cancels out).
divide both sides by 4:
a = 3/4
Let's put the value of a = 3/4 into equation I
-8 = -a + b
-8 = -3/4 + b
make b the subject of formula:
b = -3/4 + 8
b = -32 + 3
4
b = -29/4
Let's now place the values of a an b into the lines equation:
recall the lines equation is :
f(x) = ax + b
f(x) = 3/4 x - 29/4.
complete the flow proof . complete parts a. through d.
KS is common in both the triangles
so, to complete SSS rule KS = KS will be the answer.
so the answer is b
What is -1.47 rounded to four decimal places as needed?
Given the negative number
[tex]-1.47[/tex]Four decimal places implies there should be four digits after the decimal point. in the absence of no digit, add zero to complete the number of required decimal place. To round the number above to four decimal places, we will have
[tex]-1.4700[/tex]Hence, -1.47 rounded to four decimal places is -1.4700
Sphere 6.2 in diameter
ANSWER:
128.84 cubic inches.
STEP-BY-STEP EXPLANATION:
We have that the volume of a sphere is given by the following equation:
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]The radius equals half the diameter, therefore we can calculate the radius as follows:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{6.2}{2} \\ r=3.1 \\ \text{replacing and we calculate the volume:} \\ V=\frac{4}{3}\cdot\frac{22}{7}\cdot3.1^3 \\ V=128.84 \end{gathered}[/tex]The volume of the sphere with the diameter of 6.2 is 128.84 cubic inches.
what digit is in the thousands place 506,234
The thousands place is corresponding to the digit that if fourth from the unit.
So the digit in the thousands place of 506,234 is 6.
Given a planar trapezoid ABCD whose height is BE. It is known that AB = 8cm A = 60 *, find the height ofthe trapezoid.
Solution:
Given the trapezoid:
To solve for the height of the trapezoid, we use the trigonometric ratio.
From the trigonometric ratios,
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]In this case, in the triangle AEB, θ is ∠A.
Thus,
[tex]\sin A=\frac{BE}{AB}[/tex]By cross-multiplying, we have
[tex]\begin{gathered} BE=AB\times\sin A \\ =8\times\sin60 \\ =8\times\frac{\sqrt{3}}{2} \\ \Rightarrow BE=4\sqrt{3}\text{ cm} \end{gathered}[/tex]Hence, the height of the trapezoid is
[tex]4\sqrt{3\text{ }}\text{ cm}[/tex]PLEASE HELP ASAP!!! Evaluate!!!
Answer:
-5 I think
Step-by-step explanation:
Answer: -5
Step-by-step explanation:
1. Since f(-1) is -1, substitute it into the x's of the equation. The question would now be 4(-1)^2+5(-1)-4.
2. Solve and it would be -5
hi! how do i find surface area of a cylinder? for some reason i can’t get the right answer
Use the formula above to find the surface area of a cylinder.
For the given cylinder the given data is the height (6mi) and diameter (16mi), use the diameter to find the radius:
[tex]\begin{gathered} r=\frac{d}{2} \\ \\ r=\frac{16mi}{2}=8mi \end{gathered}[/tex]Surface area:
[tex]\begin{gathered} SA=2\pi(8mi)\placeholder{⬚}^2+2\pi(8mi)(6mi) \\ SA=128\pi mi^2+96\pi mi^2 \\ SA=224\pi mi^2 \end{gathered}[/tex]Then, the surface area of the given cylinder is: 224π square milesConvert the angle 225° from degrees to radians. Enter your answer in terms of π.
Remember that:
[tex]\pi\text{ rad}=180^{\circ}[/tex]Dividing both sides by 180° we get:
[tex]\frac{\pi\text{ rad}}{180^{\circ}}=1[/tex]Which we can use as conversion factor to convert degrees to radians.
For an angle of 225°:
[tex]225^{\circ}=\frac{\pi\text{ rad}}{180^{\circ}}=\frac{225}{180}\cdot\pi\text{ rad}=\frac{5}{4}\cdot\pi\text{ rad}[/tex]Therefore, in terms of π:
[tex]225^{\circ}=\frac{5}{4}\pi\text{ rad}[/tex]Sample proportion of .14 and standard deviation of.02, use empirical rule to construct a 95% confidence interval
The empirical rule states that 65% of the data under the normal curve is within 1 standard deviation of the mean, 95% of the data is within 2 standard deviations of the mean, and 99% is within 3 standard deviations of the mean.
The approximation to the distribution of the sample proportion has the following shape:
[tex]\hat{p}\approx(p;\frac{p(1-p)}{n})[/tex]The mean of the distribution is the sample proportion: μ= p
The standard deviation of the distribution is the square root of the variance
σ=√[p(1-p)/n]
For the given distribution:
μ= 0.14
σ= 0.02
95% of the distribution is μ ± 2σ
Upper bound:
[tex]\mu+2\sigma=0.14+2\cdot0.02=0.18[/tex]Lower bound:
[tex]\mu-2\sigma=0.14-2\cdot0.02=0.10[/tex]The 95% confidence interval is [0.10;0.18]
1) What is the remainder when 3x3 - 4x2 - 14x + 3 is divided by3x+5?A)A.43B)wiu0WI)D)IM
SOLUTION
The given polynomail is
[tex]3x^3-4x^2-14x+3[/tex]To be divided by
[tex]3x+5[/tex]Since the question requires to find the remainder
Then following remainder theorem
Set 3x+5 to zero and solve for x
[tex]\begin{gathered} 3x+5=0 \\ x=-\frac{5}{3} \end{gathered}[/tex]Substitute x=-5/3 into the given polynomial to get the remainder
[tex]\begin{gathered} 3(-\frac{5}{3})^3-4(-\frac{5}{3})^2-14(-\frac{5}{3})+3 \\ =3(-\frac{125}{27})-4(\frac{25}{9})+14(\frac{5}{3})+3 \\ =-\frac{125}{9}-\frac{100}{9}+\frac{70}{3}+3 \\ =\frac{-125-100+210+27}{9} \\ =\frac{12}{9} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the remainder is
[tex]\frac{4}{3}[/tex]Solve the system using graphing, substitution or elimination. If needed round soulutions to the nearest tenth
Given
The system of equations,
[tex]\begin{gathered} 9x+y=45\text{ \_\_\_\_\_\lparen1\rparen} \\ x^3-3x^2-25x+93=y\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]To find the solution.
Explanation:
It is given that,
[tex]\begin{gathered} 9x+y=45\text{ \_\_\_\_\_\lparen1\rparen} \\ x^3-3x^2-25x+93=y\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]From (1),
[tex]y=45-9x[/tex]Substitute y in (2).
Then,
[tex]\begin{gathered} x^3-3x^2-25x+93=45-9x \\ x^3-3x^2-25x+9x+93-45=0 \\ x^3-3x^2-16x+48=0 \\ x^2(x-3)-16(x-3)=0 \\ (x-3)(x^2-16)=0 \\ (x-3)(x^2-4^2)=0 \\ (x-3)(x-4)(x+4)=0 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} x-3=0,x-4=0,x+4=0 \\ \text{ }x=3,\text{ }x=4,\text{ }x=-4 \end{gathered}[/tex]Therefore, for x=3,
[tex]\begin{gathered} y=45-9\times3 \\ =45-27 \\ =18 \end{gathered}[/tex]For x=4,
[tex]\begin{gathered} y=45-9\times4 \\ =45-36 \\ =9 \end{gathered}[/tex]For x=-4,
[tex]\begin{gathered} y=45-(9\times-4) \\ =45+36 \\ =81 \end{gathered}[/tex]Hence, the solution set is (3,18), (4,9), (-4,81).
Brad is going to send some flowers to his wife. Silvergrove Florist charges $3 per rose, plus $20 for the vase. Noah's Flowers, in contrast, charges $1 per rose and $30 for the vase. If Brad orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be?Write a system of equations, graph them, and type the solution.
To solve this exercise we must first identify our variables
• C, = Total cost
,• r ,= number of roses
,• v ,= number of vases
Now, with these variables we will formulate the equations that model the price of each of the flower shops. We have to take into account that Brad is only going to buy one vase
[tex]v=1[/tex]Silvergroce Florist
[tex]\begin{gathered} C=3r+20v \\ C=3r+20(1) \\ C=3r+20\to(1) \end{gathered}[/tex]Noah's Flowers
[tex]\begin{gathered} C=1r+30v \\ C=r+30(1) \\ C=r+30\to(2) \end{gathered}[/tex]We have two equations (1) and (2), to find the total cost that is the same in both flower shops, we only have to equal them to find the number of roses that Brad should buy
[tex]\begin{gathered} 3r+20=r+30 \\ 3r-r=30-20 \\ 2r=10 \\ r=\frac{10}{2} \\ r=5 \end{gathered}[/tex]Brad must buy 5 roses so that it costs the same at both florists. To know the cost we substitute in any equation (1) or (2) the number of roses
[tex]\begin{gathered} C=r+30 \\ C=5+30 \\ C=35 \end{gathered}[/tex][tex]\begin{gathered} C=3r+20 \\ C=3(5)+20 \\ C=15+20 \\ C=35 \end{gathered}[/tex]The total cost for 5 roses and a vase is $35Answer:
y = 20 + 3x
y = 30+x
( 5,35)
Step-by-step explanation:
Writing and solving a system of equations
Silvergrove Florist: 20 + 3x
Noah's Flowers: 30 + 1x where x is the number of roses
We want to know when they are equal
20+3x = 30+1x
Subtract x from each side
20+3x-x = 30+x-x
20+2x = 30
Subtract 20 from each side
20+2x-20 = 30-20
2x = 10
Divide by 2
2x/2 = 10/2
x = 5
The number of roses is 5
The cost is
30 +x = 30+5 = 35
(5,35)
Students are asked to add one tenth and 0.1. Several different answers were submitted: 1.1, 0.11, 0.2, 0.21, and 10.1. For each response, write a decimal number sentence that would produce that answer.
The wording for the decimal will be:
1.1 = one point one
0.11 = zero point eleven
0.2 = zero point two
0.21 = zero point two one
10.1 = ten point one
How to explain the decimal?It is important to note that a decimal simply means the number that's made of a whole number and a fraction.
From example 10.1 in wordings will be ten point one. In this case, the students are asked to add one tenth and 0.1. The decimals have been given in words above.
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Use it in a lot and it can take forever
Part 1
Remember that
The rate of change is the same that the first derivative
so
The rate of change appears to be zero at times
t=1 weeks
t=4 weeks
t=6 weeks
Part 2
which of the following is true?
Verify each option
W'(3) > W'(7) -----> is not true
W'(3) < W'(7) -----> is trueW'(3)=W'(7) is not true
which of the following is true?
Verify each option
W'(0) < W'(5) -----> is truetherefore
the graph is
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
The amount earned, calculated using the formula for geometric progressions are as follows;
(A) The income on day 31 =$1,073,741,824
(B) Total income for 31 working days = $2,147,483,647
What is a geometric progression?A geometric progression is one in which each subsequent term is a constant multiple of the previous term
(A) The function that indicates the amount earned on the nth day is the formula for a geometric progression , which can be presented as follows;
[tex]a_n = a_1\cdot r^{n-1}[/tex]
The sum is presented as follows;
[tex]S_n =a_1\cdot \dfrac{1 - r^n}{1 - r}[/tex]
Therefore;
The common ratio, r = 2
The first term, a₁ = 1
The amount received on day 31 is therefore;
[tex]a_{31} = 1\times 2^{31-1} = 1,073,741,824[/tex]
Income on day 31 = $1,073,741,824
(B) The total income in 31 days is therefore;
[tex]S_{31} =a_1\cdot \dfrac{2^{31} - 1}{2- 1}== 2,147,483,647[/tex]
The total income in 31 working days = $2,147,183,647
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Mackenzie has a bag that contains 6 red marbles, 4 blue marbles, and 14yellow marbles. If she chooses one marble from the bag, what is theprobability that the marble is not yellow?O A. 7/ 금B.LINdC.soOD.
Probability that the marble is not yellow = 5/12
Explanations:Number of red marbles, N(Red) = 6
Number of blue marbles, N(Blue) = 4
Number of yellow maebles, N(Yellow) = 14
Total number of marbles, N(Total) = N(Red) + N(Blue) + N(Yellow)
N(Total) = 6 + 4 + 14
N(Total) = 24
Probability that the marble chosen is yellow, P(yellow) = N(yellow) / N(Total)
P(yellow) = 14/24
P(yellow) = 7/12
P(yellow) + P(not yellow) = 1
P(not yellow) = 1 - P(yellow)
P(not yellow) = 1 - 7/12
P(not yellow) = 5/12
Probability that the marble is not yellow = 5/12
what is the distance between -1 1/2 +5. Find absolute value
To find the absolute value of -1 1/2 +5 you make the addition:
You can write the mixed number also as -3/2 (because -1 is equal to -2/2 and -2/2 and 1/2 is -3/2).
You add fractions as follow:
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex]You can write the 5 as 5/1:
[tex]-\frac{3}{2}+\frac{5}{1}=\frac{-3\cdot1+5\cdot2}{2\cdot1}=\frac{-3+10}{2}=\frac{7}{2}[/tex]As the addition of the given numbers is 7/2, the absolute value or the distance is:
[tex]\lvert\pm a\rvert=a[/tex][tex]\lvert-1\frac{1}{2}+5\rvert=\lvert\frac{7}{2}\rvert=\frac{7}{2}[/tex]Then, the distance is 7/219.Solve the inequality. Express your answer in the form of a graph and in interval notation. (x-3) / (x+6) ≤ 0
The inequality is given as,
[tex]\frac{x-3}{x+6}\leq0[/tex]Note that the denominator can never be zero otherwise the rational function would become indeterminate. So we have to exclude the value at which the denominator,
[tex]\begin{gathered} x+6=0 \\ x=-6 \end{gathered}[/tex]So the function is not defined at x = - 6.
Consider that the division of the numbers can be non-positive, only if exactly one of the numbers is non-positive.
So we have to obtain the interval in which one of the factors is positive and the other is negative.
CASE-1: When the numerator is positive and the denominator is negative,