Given that:
- Marc sold 500 tickets for the school play.
- Student tickets cost $2.
- Adult tickets cost $5.
- The total amount of money from the sale was $1,789.
a.) Let be "x" the number of student tickets Marc sold for the school play, and "y" the number of adult tickets Marc sold for the school play.
You can represent the total number of tickets he sold with this equation:
[tex]x+y=500[/tex]You can represent the total amount of money from the sale with this equation:
[tex]2x+5y=1789[/tex]Now you can set up this System of Equations that can be used to determine how many of each type of ticket Marc sold:
[tex]\begin{cases}x+y={500} \\ 2x+5y={1789}\end{cases}[/tex]b.) You can solve the System of Equations using the Elimination Method:
1. Multiply the first equation by -2:
[tex]\begin{cases}(-2)(x+y)=(-2)({500)} \\ 2x+5y={1789}\end{cases}[/tex][tex]\begin{cases}-2x-2y={-1000} \\ 2x+5y={1789}\end{cases}[/tex]2. Add the equations:
[tex]\begin{gathered} \begin{cases}-2x-2y={-1000} \\ 2x+5y={1789}\end{cases} \\ ---------- \\ 0+3y=789 \\ 3y=789 \end{gathered}[/tex]3. Solve for "y":
[tex]\begin{gathered} y=\frac{789}{3} \\ \\ y=263 \end{gathered}[/tex]4. Substitute the value of "y" into the first original equation and solve for "x":
[tex]\begin{gathered} x+263=500 \\ x=500-263 \\ x=237 \end{gathered}[/tex]Hence, the answers are:
a.)
[tex]\begin{cases}x+y={500} \\ 2x+5y={1789}\end{cases}[/tex]b.)
[tex]x=237\text{ \lparen Number of student tickets Marc sold\rparen}[/tex][tex]y=263\text{ \lparen Number of adult tickets Marc sold\rparen}[/tex]Maddie borrowed $1500 at a 4% interest rate. If she pays off the loan in 3 years.
how much will she pay in total with interest?
$1,680
$50
$500
$180
Answer:
1680
Step-by-step explanation:
Answer:
I guess if she is Pays the money in three years, she will pay a capital of 1500/3 per year, which is 500$ per year. The Interest she pays the first year is: I=Debt*interest rate, so I=1500$*0.04, which is: I=60$. So without other information, i assume she pays 60$ each year, so in three years: I=60*3 --> 180$.
In the first week of July, a record 1,020 people went to the local swimming pool. In the second week, 105 fewer people went to the pool than in the first week. In the third week, 140 more people went to the pool than in the second week. In the fourth week,239 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
Step-by-step explanation:
huhhhhh
A certain insecticide kill 70% of all insects in a laboratory experiments A sample of 10 insects is exposed to the insecticide in a particular experiment what is the probability that exactly 3 insectswill die round your answer to four decimal places
The probability that exactly three insects will die is 0.343
Given 70% chance that an insect will die.
let A be the event that 1 insect dies.
P(A) = 0.7
The probability that the insect will not stay alive
= 1 - P(A)
= 1 - 0.7
= 0.3
Now there is a sample of 10 insects that are affected by the insecticide.
Therefore number of ways exactly 3 insects will die using binomial distribution is
= 10C3 × (0.7)³ × (0.3)⁷
= 120 × (0.7)³ × (0.3)⁷
=0.00901
≈ 0.009
Hence the required probability is 0.009 .
A probability distribution is an idealised frequency distribution. The frequency distribution of a certain sample or dataset serves as a description of it.
It is the frequency with which each conceivable value of the variable appears in the dataset. How frequently a value emerges in a sample is determined by its probability of occurrence.
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For f(x) and g(x), describe each transformation. Then write the equation of the transformed function. f(x)=2x+1 g(x)=1/3x+2
I am haveing a very hard time figuring this out due to my dyscalculia
The transformation processes and equation of the transformed function are:
a) f(x) is translated in the negative y direction and the equation of the transformed function is f(x) = 2x - 4
b) g(x) is translated in the positive y direction and the equation is g(x) = 1/3x + 6
c) g(x) is dilated 3 times hat it as and the equation is x + 6
d) f(x) is dilated and the equation is x + 1/2
What is Dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
f(x) is translated by 5 units to the negative y-direction, so f(x) - 5 becomes 2x + 1 -5 = 2x - 4
g(x) + 4 means translation 4 units to the positive y-axis and the function g(x) + 4 becomes x/3 + 2 + 4 = x/3 + 6
3g(x) is dilation which means g(x) would be 3 times what it was initially.
3 x ( x/3 + 2) = x + 6
1/2f(x) is dilation which is a reduction by half. so the function becomes
1/2 x ( 2x + 1) = x + 1/2
In conclusion, the transformation processes are:
a) f(x) is translated in the negative y direction and the equation of the transformed function is f(x) = 2x - 4
b) g(x) is translated in the positive y direction and the equation is g(x) = 1/3x + 6
c) g(x) is dilated 3 times hat it as and the equation is x + 6
d) f(x) is dilated and the equation is x + 1/2
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find the image of (-2,-9) after a reflection over the y-axis
Which equation represents the line that is perpendicular to y = 1/6 and passes through (-8,-2)?
Answer:
If it is perpendicular: mperp..=-1/m, so:
mperpendicular= -6.
formula of the line passing through one point:
y-y0=m(x-x0)
so: y+2=-6(x+8)
y=-6x+48-2
y=-6x+46 is the answer
need some help pls due date 10pm
thanks to whoever answers
Answer:
x = 90°
y = 20°
z = 20°
Step-by-step explanation:
Each interior angle of a square is 90°.
Angles on a straight line sum to 180°.
Angle x
⇒ 90° + x = 180°
⇒ 90° + x - 90° = 180° - 90°
⇒ x = 90°
Angle z
⇒ z + 90° + 70° = 180°
⇒ z + 160° = 180°
⇒ z + 160° - 160° = 180° - 160°
⇒ z = 20°
Interior angles of a triangle sum to 180°.
Angle y
⇒ x + 70° + y = 180°
⇒ 90° + 70° + y = 180°
⇒ 160° + y = 180°
⇒ 160° + y - 160° = 180° - 160°
⇒ y = 20°
8) -14x-7y - 18
-6x-3y-6
I need help badly
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
What is the total surface area ratio of following similar solids?30 mi45 mi60 mi90 mi09:4O 15:6O 5:4O 3:2
Solid A has five(5) rectangular blocks that are co-joined. The dimension of each, is 45miles by 90miles.
Thus,
[tex]\begin{gathered} Total\text{ surface area=5}\times Area\text{ of one rectangular block} \\ \text{Total Surface Area=5}\times(45\times90) \\ T\mathrm{}S\mathrm{}A=5\times4050 \\ T\mathrm{}S\mathrm{}A=20250mi^2 \end{gathered}[/tex]Solid B has five(5) rectangular blocks that are co-joined. The dimension of each, is 30mi by 60mi.
Thus,
[tex]\begin{gathered} \text{Total Surface Area= 5}\times Area\text{ of one rectangular block} \\ T\mathrm{}S\mathrm{}A=5\times(30\times60) \\ T\mathrm{}S\mathrm{}A=5\times1800 \\ T\mathrm{}S\mathrm{}A=9000mi^2 \end{gathered}[/tex]The ratio of the T.S.A of the similar solids is given below:
[tex]\begin{gathered} T\mathrm{}S\mathrm{}A_{solid\text{ A}}\colon T.S.A_{solid\text{ B}} \\ 20250\colon9000 \\ \text{Divide both by 2250, we have:} \\ 9\colon4 \end{gathered}[/tex]Hence, the correct option is Option A
Question 1(Multiple Choice Worth 2 points)
(Converting Between Systems MC)
For a craft project you need 182 inches of ribbon, but it is only sold by the meter. Determine the amount of ribbon, in meters, you need to buy for the project. (1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter)
462
47
12
5
Using the conversion method, 4.6228 meter ribbon we need for craft project.
In the given question,
For a craft project you need 182 inches of ribbon, but it is only sold by the meter.
We have to determine the amount of ribbon, in meters.
As given 1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter.
Firstly we know that inches, meters and centimeters all are units to measure the length.
Since we know that in 1 inch have 2.54 centimeters and 1 centimeters have 0.01 meter.
So we firstly convert the 2.54 centimeters in meter.
1 centimeter = 0.01 meter
2.54 centimeter = 2.54×0.01 meter
2.54 centimeter = 2.54×0.01 meter
2.54 centimeter = 0.0254 meter
So we can say that
1 inch = 0.0254 meter
We have to by 182 inches of ribbon. So
182 inches = 0.0254×182 meters
182 inches = 4.6228 meters
Hence, 4.6228 meter ribbon we need for craft project.
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Out of 20 attempts a basket ball player only scored 8 times what percent of his chances did he score?
Answer:
40%
Step-by-step explanation:
20 x 5 = 100
8 x 5 = 40
Which means 8 out of 20 is 40% of 20.
Write the equation in Slope-Intercept form that passes through the point (-4, -9) and has a slope of 1/12.
Answer:
[tex]y=\frac{1}{12}x-\frac{26}{3}[/tex]
Step-by-step explanation:
[tex]y+9=\frac{1}{12}(x+4) \\ \\ y+9=\frac{1}{12}x+\frac{1}{3} \\ \\ y=\frac{1}{12}x-\frac{26}{3}[/tex]
?
Find the Area of the figure below, composed of a rectangle and a semicircle. The
radius of the circle is shown. Round to the nearest tenths place.
Area of Irregular Shapes
Nov 03, 2-44:03 PM
Answer:
9
3
100 POINTS PLEASE HELP !!!!!
Answer:
50.3 square units
Step-by-step explanation:
area of rectangle: 11 x twice the radius
radius = 2
A(rect): = 11(4) = 44 sq units
A (semi-circle) = (π·r²) / 2
A = 4π / 2 = 2π = 6.28 sq units
44.0 + 6.28 = 50.28
Answer:
68.1
Step-by-step explanation:
3.14*3²=28.26
28.26/2=14.13
3*2=6
9*6=54
54+14.13=68.13
68.1
which of the following expression is equivalent to 7 y + 21 y(7+21) 7(y+21). 7(y+3. 21y+7
The expression given is;
[tex]\begin{gathered} 7y+21 \\ \text{The equivalent is;} \\ =7(y+3) \\ We\text{ use 7 to factor both sides of the expression, hence} \\ \frac{7y}{7}=y \\ \text{And} \\ \frac{21}{7}=3 \\ \text{Therefore, the answer is } \\ 7(y+3) \end{gathered}[/tex]The correct answer is option C
I need help with this question. I don’t know how to do this.
Solution:
The arithmetic sequence is given below as
[tex]19,24,29,34,...[/tex]Step 1:
We will calculate the common difference using the formula below
[tex]\begin{gathered} d=t_2-t_1=t_3-t_2 \\ d=24-19=29-24 \\ d=5 \end{gathered}[/tex]Step 2:
We will calculate the fifth term using the formula below
[tex]\begin{gathered} c \\ n=5,a=19,d=5 \\ t_5=19+(5-1)5 \\ t_5=19+20 \\ t_5=39 \end{gathered}[/tex]We will calculate the sixth term using the formula below
[tex]\begin{gathered} t_n=a+(n-1)d \\ n=6,a=19,d=5 \\ t_6=19+(6-1)5 \\ t_6=19+25 \\ t_6=44 \end{gathered}[/tex]We will calculate the seventh term using the formula below
[tex]\begin{gathered} t_7=a+(n-1)d \\ n=7,a=19,d=5 \\ t_7=19+(7-1)5 \\ t_7=19+30 \\ t_7=49 \end{gathered}[/tex]Hence,
The next three terms of the arithmetic sequence are given below as
[tex]\Rightarrow39,44,49[/tex]Can you help me with this one please? Only part b
Simplifying,
[tex]\begin{gathered} ((5+2i)^2-2)i\rightarrow(25+20i+4i^2-2)i\rightarrow(23+20i-4)i \\ \\ \rightarrow(19+20i)i\rightarrow19i+20i^2\rightarrow-20+19i \end{gathered}[/tex]A scientist observes and counts 155 bacteria in a culture. Later, the scientist counts again and finds the number has increased as shown.
Answer:
You multiply 155 by 0.40 which is 40% and you get 62 then you add 62 to 155 and your final count of bacteria is 217
Step-by-step explanation:
Use the model of the rectangular prism to answer the question. The width of the
prism is (2x - 2) ft, and its height is (x + 7) ft. The area of the base of the prism is
(3x2 + 3x - 4) ft².
Could the length of b be (3x - 1) ft? Complete the explanation.
Answer:
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
Step-by-step explanation:
Given dimensions of a rectangular prism:
Width = (2x - 2) ftHeight = (x + 7) ftArea of the base = (3x² + 3x - 4) ft²The area of the base of a rectangular prism is the product of the width of the base and the length of the base.
To determine if length b could be (3x - 1) ft, multiply b by the width of the base of the prism.
[tex]\begin{aligned}\implies \sf Area\;of\;base&=\sf length \times width\\&=b \times (2x-2)\\&=(3x-1)(2x-2)\\&=3x(2x-2)-1(2x-2)\\&=6x^2-6x-2x+2\\&=6x^2-8x+2\end{aligned}[/tex]
Therefore, the length of b cannot be (3x - 1) as the area of the base when b is (3x - 1) is not equal to the given area of the base.
[tex]\textsf{$\boxed{\sf No}$\;. The area of the bottom face of the prism is $(3x^2+3x-4)\; \sf ft^2$, and the product}[/tex]
[tex]\textsf{of $(3x-1)$\;ft\;and $\left(\; \boxed{2}\:x-\boxed{2}\;\right)$ ft\;is\;$\left(\; \boxed{6}\:x^2-\boxed{8}\:x+\boxed{2}\;\right)$\;ft$^2$.}[/tex]
if a || b, m<2=63°, and m<9=105°, find the measure of missing angle m<1=?
Given:
a.) ∠9 = 105°
b.) ∠2 = 63°
Step 1: Determine the measure of ∠10.
∠9 and ∠10 are Supplementary Angles. This means that the sum of the two angles is equal to 180°.
From this, we generate the following equation:
[tex]\text{ }\angle9\text{ + }\angle10=180^{\circ}[/tex]Let's then now proceed to find out the measure of ∠10.
[tex]\text{ }\angle9\text{ + }\angle10=180^{\circ}[/tex][tex]\text{ }105^{\circ}\text{ + }\angle10=180^{\circ}[/tex][tex]\angle10=180^{\circ}\text{ - }105^{\circ}[/tex][tex]\angle10=75^{\circ}[/tex]Step 2: Determine the measure of ∠3.
∠10 and ∠3 are Alternate Exterior Angles. Under this, the two angles must be congruent.
[tex]\text{ }\angle3\text{ = }\angle10[/tex]Therefore,
[tex]\text{ }\angle3\text{ = }\angle10[/tex][tex]\text{ }\angle3=75^{\circ}[/tex]Step 3: Determine the measure of ∠1.
∠1, ∠2 and ∠3 are also Supplementary Angles. This means that the sum of the three angles is equal to 180°.
Thus, we generate the equation below:
[tex]\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}[/tex]Let's now find the measure of ∠1,
[tex]\text{ }\angle1\text{ + }\angle2\text{ + }\angle3=180^{\circ}[/tex][tex]\text{ }\angle1\text{ + }63^{\circ}\text{ + }75^{\circ}=180^{\circ}[/tex][tex]\text{ }\angle1\text{ + }138^{\circ}=180^{\circ}[/tex][tex]\text{ }\angle1\text{ }=180^{\circ}\text{ - }138^{\circ}[/tex][tex]\text{ }\angle1\text{ }=42^{\circ}[/tex]Therefore, the measure of ∠1 is 42°.
Find the measure of 44.
72° 118°
118°
44
44 =
[?]°
Enter
The measure of angle 4 is 72°
We can observe that we have been given two parallel lines intersected by a transversal.
We need to find the measure of angle 4.
We can observe that angle which measures 72 degrees angle 4 are corresponding Angles.
We know that the Corresponding Angles are congruent.
Therefore, the measure of angle 4 is 72°
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how do I find all of the following that can be a counterexample for the statement below?
As we need to select counterexamples, we have to select all the options that make the statement x+2>7 a FALSE statement.
Then, we can rearrange:
[tex]\begin{gathered} x+2>7 \\ x>7-2 \\ x>5 \end{gathered}[/tex]We have to select all the options where x is NOT greater than 5: -2, 0, 3, 4.
The options -2, 0, 3, 4 have to be selected.
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A portion of a hiking trail slopes upward at about a 6° angle.To the nearest tenth of a foot, what is the value of x, thehiker's change in vertical position, if he has traveled a
In the given right triangle ABC
we have that
[tex]tan(C=\frac{AB}{AC}\text{ ----> by TOA}[/tex]substitute given values
[tex]\begin{gathered} tan(6^o)=\frac{x}{120} \\ \\ x=120*tan(6^o) \\ x=12.6\text{ ft} \end{gathered}[/tex]The answer is the option Bwhat is the slope of a line that passes through the two points (8,3) nd (4,9)?
Given the points (8,3) and (4,9), we can find the slope of the line that passes through them with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, we have the following:
[tex]undefined[/tex]25 over 23 as a decimal rounded to the nearest hundredth
Answer:
1.09
Step-by-step explanation:
25/23 is the same thing as 25 divided by 23
Once you get answer round to nearest hundreth
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)[/tex]
Solve the inequality
6(x/2+4)≥9
3x+24=9
3x=9-24
3x=-15
x=-5
Angela and Barry share a piece of land. The ratio of the area of Angela’s portion to the
area of Barry’s portion is 3:2. They each grow corn and peas on their piece of land. The
entire piece of land is covered by corn and peas in the ration 7:3. On the Angela’s portion
of the land, the ratio of corn to peas is 4:1. What is the ratio of corn to peas for Barry’s portion?
(A)11:9 (B)2:3 (C)3:2 (D)3:7 (E)1:4
Answer:
3:2
Step-by-step explanation:
Angela + Barry = land
7 corn + 3 peas = land
4 corn + 1 peas = Angela
land = land
Angela + Barry = 7 corn + 3 peas
4 corn + 1 peas + Barry = 7 corn + 3 peas
Barry = 7 corn + 3 peas - 4 corn - 1 peas
Barry = 3 corn + 2 peas
Barry = 3:2
The ratio of corn to peas for Barry's portion is 3:2. Hence, option C is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data given in the question,
Angela + Barry = land
7 corn + 3 peas = land
4 corn + 1 peas = Angela
land = land
Angela + Barry = 7 corn + 3 peas
4 corn + 1 peas + Barry = 7 corn + 3 peas
Barry = 3 corn + 2 peas
Barry = 3:2
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how do I do this on a line?[tex]3 \ \textless \ 2x - 3 \leqslant 13[/tex]
Let the inequality:
[tex]3\text{ }<\text{ 2x - 3}\leq\text{ 13}[/tex]1. we add + 3 :
[tex]3\text{ +3}<\text{ 2x }\leq\text{ 13}+3[/tex]this is equivalent to :
[tex]6<\text{ 2x }\leq\text{ 1}6[/tex]we resolve for x ( we divide by 2) :
[tex]3<\text{ x }\leq8[/tex]that is the interval:
[tex](3,\text{ 8}\rbrack[/tex]on the real line, the interval is:
On the other hand, the inequality:
[tex]-2\text{ }<\frac{3+x}{4}\leq\text{ 3}[/tex]
1. Multiply by 4:
[tex]-8\text{ }<3+x\leq12[/tex]2. Add -3:
[tex]-11\text{ }that is the interval:[tex](-11,\text{ 9}\rbrack[/tex]
on the real line, the interval is: