Answer:
5/33
Step-by-step explanation:
5/12 * 4/11 = 20 /132 = 10 / 66 = 5 / 33
The probability of drawing a red marble on the first try is 5/12 because there are 5 red marbles and 12 marbles in total. The second time you only have 4 red marbles left and 11 marbles left in total. Multiply them to find the probability of drawing 2 red marbles in a row.
Probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Here,
Number of red marbles = 5 marble
Number of green marbles = 7 marble
Probability = Number of favorable outcome / Number of total outcome
Probability of drawing 1 red marble = [tex]\frac{5}{12}[/tex]
Probability of drawing second marble is red = [tex]\frac{4}{11}[/tex]
Probability of drawing 2 red marbles = [tex](\frac{5}{12})(\frac{4}{11} )=\frac{5}{33}[/tex]
Hence, the probability of drawing 2 red marble is [tex]\frac{5}{33}[/tex]
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What is the volume of a cylinder with a radius of five and a height of three
The t value for a 95% confidence interval estimation with 24 degrees of freedom is
Answer: the value us 2.064
Step-by-step explanation:
To determine the t value, we would need the t distribution table. Since degree of freedom is known as 24, we would determine alpha/2
A 95% confidence level is 95/100 = 0.95
1 - alpha = 0.95
alpha = 1 - 0.95
alpha = 0.05
alpha/2 = 0.05/2 = 0.025
this is the area to the left. The area to the right 1 - 0.025 = 0.975
alpha/2 = 0.975
Looking at the t distribution table, the t value is
2.064
What is the missing side 7.5 in and x
Answer:
The missing side is 18 inches
Step-by-step explanation:
Since in the smaller rectangle the sides are 2.5in x 6in and one side for the larger rectangle is given, you can make an equation.
[tex]\frac{2.5}{6}=\frac{7.5}{x}[/tex]
Then you can cross multiply.
2.5x=45
Divide by 2.5 on both sides.
x= 18
Answer:
18
Step-by-step explanation:
if it is a ratio like 2.5:6 the the answer will be 18 because if you do 2.5 over 7.5 that comes out to a total of 0.33 and thats rounded so if you do 6 over .33 then the answer will be 18
Countries with low GDPs are the most highly developed countries in the world.
Please select the best answer from the choices provided.
T
F
A book store earned $235 in sales for 4 copies of a new cookbook and 5 copies of a new science fiction novel. The next day it earned $180 in sales for 3 copies of the cookbook and 4 copies of the science fiction novel. What was the price of each book?
The price of the cookbook is $40, and the price of the science fiction novel is $15. This was determined by setting up and solving a system of equations based on the sales data provided for two different days.
The student has asked to determine the price of each book based on the sales data for two days. This is a system of equations problem in which we have two equations with two unknowns, representing the prices of two different books. Let's denote C as the price of the cookbook and S as the price of the science fiction novel. From the information given:
4C + 5S = 235 (sales on the first day).
3C + 4S = 180 (sales on the second day).
By solving these two equations simultaneously, we can find the exact prices for both books.
Step 1: Multiply the second equation by 4/3 to align the coefficient of C with the first equation:
([tex]\frac{4}{3}[/tex])(3C + 4S = 180)
4C + ([tex]\frac{16}{3}[/tex])S = 240
Step 2: Subtract the first equation from this new equation:
[([tex]\frac{16}{3}[/tex])S - 5S] = [240 - 235]
[tex]S = \frac{5 }{ \frac{16}{3} - \frac{15}{3}}[/tex]
[tex]S = \frac{5 }{ \frac{1}{3}}[/tex]
S = $15 (price of the science fiction novel)
Step 3: Substitute the value of S in one of the original equations to find C:
3C + 4(15) = 180
3C + 60 = 180
3C = 120
C = $40 (price of the cookbook)
Given the equation f(x) = (x + 3)2 – 8, fill in the blanks: Axis of symmetry: x = _______a0 Vertex: ( _______a1, _______a2) Number of real solutions: ________a3
We have been given an equation [tex]f(x)=(x+3)^2-8[/tex]. We are asked to fill in the blanks using our given equation.
The axis of symmetry will be the vertical line passing through vertex.
First of all, we will convert our given equation in standard vertex form of parabola as:
Standard vertex form of parabola: [tex]y=(x-h)^2+k[/tex], where (h,k) is vertex of parabola.
[tex]f(x)=(x-(-3))^2-8[/tex]
Upon comparing our function with standard vertex form, we can see that vertex of parabola is at [tex](-3,-8)[/tex].
The axis of symmetry will be vertical line passing through point [tex](-3,-8)[/tex]. The vertical line will pass through [tex]x=-3[/tex], therefore, the axis of symmetry is [tex]x=-3[/tex].
Since our given parabola is an upward opening parabola, so it has a minimum at [tex](-3,-8)[/tex]. This means that parabola will intersect the x-axis at two points. Therefore, there are two real solutions for the given function.
a regular pentagon has a perimeter of 60 cm what is the measure of angle CBD
The measure of angle CBD in a regular pentagon with perimeter 60 cm is 108°. This conclusion assumes that CBD refers to an internal angle of the pentagon and is based on the formula for internal angles of a regular polygon.
Explanation:The subject of the question is related to a regular pentagon which is a polygon with 5 equal sides and equal angles. If the perimeter of the regular pentagon is 60 cm, it means each side measures 60/5 = 12 cm.
The question is asking for the measure of angle CBD. In a regular pentagon, angles are not directly named but it's likely referring to an internal angle of the pentagon. Based on this assumption, we can calculate the measure of an internal angle of a regular polygon using the formula: (n-2) x 180° / n where 'n' is the number of sides. Substituting '5' in place of 'n' because a pentagon has 5 sides, we get (5-2) x 180° / 5, which results in 108°. Therefore, if CBD is an internal angle then it measures 108 degrees.
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3 (4y + 1) + 2y what is the answer?
Step-by-step explanation:
12y + 3 + 2y
14y + 3
If you have to find the value of y then
14y = - 3
y = - 3/14
what is 8×8 ? Correct answers only !!
Answer:
64
brainliest is appreciated :))))))
Step-by-step explanation:
On a coordinate plane, a line with negative slope goes through (negative 8, 6) and (4, negative 4). A point is at (negative 6, 10).
Which is the ordered pair for the point on the x-axis that is on the line parallel to the given line and through the given point (–6, 10)?
(6, 0),(-6,10)
Step-by-step explanation:Find the slope of the first line.
Points:
A(-8, 6), B(4, -4)
m = Slope = change in y over the change in x = [tex]\frac{y2-y1}{x2-x1} = \frac{-4-6}{4-(-8)} =\frac{-10}{12} = -\frac{5}{6}[/tex]
Plug (-6, 10) into y = mx + b to get your y intercept using the same slope
Additional info: Because its parallel the slopes are the same but the only thing we need to find is the y intercept to find the equation to the second line.
y = -5/6x + b
10 = -5/6(-6) + b
10 = 5 + b
-5 -5
5 = b
Write the equation
y = -5/6x + 5
Plug in 0 for y to get your x-intercept and solve to get your second point of the ordered pair
0 = -5/6x + 5
-5 -5
-5 = -5/6x
6 = x
Your ordered pair is:
(6, 0)
Answer:
(6, 0),(-6,10)
Step-by-step explanation:
(6, 0),(-6,10)
Step-by-step explanation:
Find the slope of the first line.
Points:
A(-8, 6), B(4, -4)
m = Slope = change in y over the change in x =
Plug (-6, 10) into y = mx + b to get your y intercept using the same slope
Additional info: Because its parallel the slopes are the same but the only thing we need to find is the y intercept to find the equation to the second line.
y = -5/6x + b
10 = -5/6(-6) + b
10 = 5 + b
-5 -5
5 = b
Write the equation
y = -5/6x + 5
Plug in 0 for y to get your x-intercept and solve to get your second point of the ordered pair
0 = -5/6x + 5
-5 -5
-5 = -5/6x
6 = x
Your ordered pair is:
(6, 0)
the smith family is shopping for a new car and they are basing their decision on color and style Explain how many color choices and how many style choices they might have if there are 8 possible outcomes Justify your answer
Answer:
Sample response: The Smith family has 2 choices to make, color
and style. By the fundamental counting principle, the product of the
number of choices of color and style must equal 8. So, there could be 1
color and 8 style choices, 2 colors and 4 styles, 4 colors and 2 styles,
or 8 colors and 1 style.
Step-by-step explanation:
The smith can have 1 style and 8 colors, 2 styles and 4 colors, 4 styles and 2 colors, and 8 styles and 1 color.
What are permutation and combination?A permutation can be defined as the number of ways a set can be arranged, order matters but in combination, the order does not matter.
We have:
Smith family is shopping for a new car and they are basing their decision on color and style.
The total possible outcomes = 8
By the principle of counting the smith family has four choices.
1 style and 8 colors2 styles and 4 colors4 styles and 2 colors8 styles and 1 colorThe above are the factors of 8 because smith has a total number of 8 possible outcomes.
Thus, the smith can have 1 style and 8 colors, 2 styles and 4 colors, 4 styles and 2 colors, and 8 styles and 1 color.
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A cereal box's length is 25 cm, height is 30 cm and width is 10 cm.
The surface area of the cereal box is 2600 square centimeters. Volume of the cereal box is 7500 cubic centimeters.
The surface area of the cereal box in the image is 2600 square centimeters. The volume of the cereal box is 7500 cubic centimeters.
To calculate the surface area, we need to find the area of each of the six faces of the box and add them all up. The two largest faces have dimensions 25 cm by 30 cm, so their area is 25 * 30 = 750 square centimeters each. The two next-largest faces have dimensions 10 cm by 30 cm, so their area is 10 * 30 = 300 square centimeters each. The two smallest faces have dimensions 25 cm by 10 cm, so their area is 25 * 10 = 250 square centimeters each. Therefore, the total surface area of the box is 750 + 750 + 300 + 300 + 250 + 250 = 2600 square centimeters.
To calculate the volume, we simply multiply the length, width, and height of the box together. The length is 25 cm, the width is 10 cm, and the height is 30 cm, so the volume is 25 * 10 * 30 = 7500 cubic centimeters.
Here is a table summarizing the surface area and volume of the cereal box:
| Property | Value |
|--------------------|--------------------------------------|
| Surface area | 2600 square centimeters|
| Volume | 7500 cubic centimeters |
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Yelena has 24 apples. She packs an equal number of apples in each of b boxes. How many apples are in each box?
Answer:
Multiple possible without box count: 1,2,3,4,6,12,24
Step-by-step explanation:
Without knowing how many boxes there are you can get multiple answers
if there are 24 boxes then 1 apple goes into each box
if there are 12 boxes then 2 apples can go into each box
if there are 8 boxes then 3 apples can go into each box
if there are 6 boxes then 4 apples can go into each box
if there are 4 boxes then 6 apples can go into each box
if there are 2 boxes then 12 apples can go into each box
if there is 1 boxes then 24 apples can go into that box
with added information i can edit my answer
–2x + 2y = -4
3х + Зу = -18
Answer:
(-2, -4)
Step-by-step explanation:
–2x + 2y = -4
3х + Зу = -18
Divide the first equation by 2
–2x/2 + 2y/2 = -4/2
-x +y = -2
Divide the second equation by 3
3х/3 + Зу/3 = -18/3
x + y = -6
Add these equation together
-x +y = -2
x + y = -6
-------------------
0x + 2y = -8
2y = -8
Divide each side by 2
2y/2 = -8/2
y = -4
Now we need x
x+y = -6
x-4 = -6
Add 4 to each side
x-4+4 = -6+4
x = -2
PLEASE HELP ASAP !!!
Answer:
The total of a triangle like all the angles added together have to equal 180 degrees
2
the second answer choice
Step-by-step explanation:
115+25+35= 175
end result isn't 180 so no!
115+32+33= 180
end result is 180 so yes!
120+35+35= 190
end result isn't 180 so no!
120+30+20= 170
end result isn't 180 so no!
Jay bought 15 tee shirts for $68.40. What was the unit price of the tee shirts?????????????????????????????????????? HELP PLEASE I WILL MARK BRAINLEST
4.56
Step-by-step explanation:
Hope this helps :)
The unit price of the tee shirts that Jay bought is calculated by dividing the total cost ($68.40) by the number of tee shirts (15), coming to a unit price of $4.56 per tee shirt.
Explanation:The question is asking for the unit price of the tee shirts that Jay bought. To find the unit price, you'll divide the total price by the number of units (tee shirts) purchased. This is a straightforward division of the total cost by quantity.
So, Jay's total cost is $68.40 for 15 tee shirts. To calculate the unit price:
Divide the total cost ($68.40) by the number of tee shirts (15).The result will be the cost per shirt (unit price).So, $68.40 / 15 = $4.56.
Therefore, the unit price for the tee shirts that Jay bought is $4.56.
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2 cell phones with different text packages. Plan a: $5 per month plus 3 cents per charge. Plan b: no charge per moth plus 10 cents per text. Is there a certain number of texts when two plans cost the same? How many text on each plan to have same bill amount?
Answer:
a) No there is no certain number of texts when two plans cost the same
b) On plan A 1 text and on plan B 2 text
Step-by-step explanation:
Let us calculate the per text charge for both the plans
Plan A
Total monthly charge of the plan [tex]= 5[/tex] dollars
Number of cents is a dollar [tex]= 100[/tex]
Total cents in five dollars [tex]= 5* 100 = 500[/tex] cents
Total number of days in a month [tex]= 30[/tex]
Charge per day
[tex]= \frac{500}{30} \\= \frac{50}{3} \\= 16.67[/tex]
Now, if only one text is send in a day, the total charge of the text will be
[tex]16.67 + 3[/tex]
[tex]19.67[/tex] cents per text or [tex]20[/tex] cents per text
Plan B
No charge for the month + $ [tex]10[/tex] cents per text
[tex]=[/tex] $ [tex]10[/tex] cents per text
a) No there is no certain number of texts when two plans cost the same
b) On plan A 1 text and on plan B 2 text
Select all the expressions equivalent to 2(x + 3). Explain your reasoning. A 2 ⋅ (x + 3) B (x + 3)2 C 2 ⋅ x + 2 ⋅ 3 D 2 ⋅ x + 3 E (2 ⋅ x) + 3 F (2 + x)3
Answer: B and A
Step-by-step explanation:
(X+3)2 = 2×x + 2×3
= 2x + 6
Likewise
2(x+3) = 2×x +. 2×3
= 2x + 6
Hence they are both same
2.(X +3) still equivalent to 2x +6
Answer:
A and B
Step-by-step explanation:
In this question, we are asked to pick the options which have the same value as the expression in the question.
Firstly, let’s expand the main expression in the question.
Mathematically, expanding this, we have 2x + 6
now let’s consider the options one after the other.
Options A and B are correct as they mean the same thing and would refer to the expression in the question.
Option c is wrong. Expanding option c would yield 2x + 4
option d is wrong as the multiplication is only between 2 and x and does not cover 3. This makes the expression as 2x + 3
option E is is also wrong as it is same as D but expressed in another fashion
option F is is wrong also as expanding would give 6 + 3x which is different from 2x + 6
Jack's mother gave him 505050 chocolates to give to his friends at his birthday party. He gave 333 chocolates to each of his friends and still had 222 chocolates left. Write an equation to determine the number of friends (x)(x)(, x, )at Jack's party. Find the number of friends at Jack's party.
Answer:
There are 16 friends at Jack's party.
Step-by-step explanation:
We are given the following in the question:
Let x be the number of friends at Jack's party.
Total number of chocolates Jack have = 50
Number of chocolates given to each friend = 3
Number of chocolates left = 2
Thus, we can write the equation:
Total number of chocolate - Total number of chocolates given = Total number of chocolates left
[tex]50 - 3x = 2[/tex]
Solving the equation, we get,
[tex]50 - 3x = 2\\3x = 48\\\\\Rightarrow x = \dfrac{48}{3} = 16[/tex]
Thus, there are 16 friends at Jack's party.
What the area of a trapezoid
Answer:
A =176 cm^2
Step-by-step explanation:
The area of a trapezoid is found by
A =1/2 (b1+b2) *h
where b1 and b2 are the lengths of the bases
A =1/2(12+10) *16
A = 1/2(22)*16
A =176 cm^2
Jason filled his 52 ounce mug full of his favorite soda at the gas station it cost a total of $1.07 to fill his mug how much did Jason pay per ounce to fill his mug
Answer:
2 cents per ounce
Step-by-step explanation:
divide 1.07 by 52 to get 2 cents
What is the product?
Answer:
-6.66
Step-by-step explanation:
Answer:
-6.6 (the 6 on the right is repeating)
Step-by-step explanation:
Finding the Surface Area of a Rectangular Prism
Select Transform to change the drawing of the figure.
VA
Find the surface area of the prism. Use the net to help.
Surface area.
Surface area units
6 cm
3 cm
3 cm
2 cm
3 cm
2 cm
Transform
Intro
The surface area of the prism is 72 cm².
What is surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
We have a prism in the shape of cuboid.
length = 6 cm, Width = 3 cm, Height = 2 cm
So, Surface Area of Cuboid
= 2 (lw + wh + lh)
= 2 ( 18 + 6 + 12)
= 2 (36)
= 72 cm²
Thus, the surface area of prism is 72 cm².
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How is the slope of the line related to the arithmetic sequence
Answer:
b) It is the common difference.
Step-by-step explanation:
In arithmetic sequence the difference between one term and other term is constant. The slope of the line related to the arithmetic sequence is Common Difference.
What is arithmetic sequence?In arithmetic sequence the difference between one term and other term is constant
We need to find how slope of the line related to the arithmetic sequence.
A common difference is a difference between any term and its preceding term in an arithmetic sequence. The slope of the line related to the arithmetic sequence is common difference.
Therefore common difference is related to arithmetic sequence.
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Jim's backyard is a rectangle that is 12 5 6 yards long and 10 2 5 yards wide. Jim buys sod in pieces that are 1 1 3 yards long and 1 1 3 yards wide. How many pieces of sod will Jim need to buy to cover his backyard with sod?
Answer: 75
Step-by-step explanation:
Step-by-step explanation:
In order to cover his backyard with sod, he needs to cover the area of the backyard.
His backyard is a rectangle, and area of a rectangle represented by A is given as l*w
Where,
is the length, and
is the width
So, the area of Jim's backyard is square yards.
l*w=12/5/6*10/2/5=2002/15 or 133.466
The area of each sods are solved using the area of the rectangle formula.
l*w=1/1/3*1/1/3=16/9
To find HOW MANY of these sods we would need to cover the whole backyard, we divide the backyard area by each sod area:
=2002/15 divided by 16 /9=3003/40or 75.075
Since, fractional sods can't be bought, Jim has to buy 75 sods approximately .
An aquarium tank can hold liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in minutes. The second pipe can fill the tank in minutes by itself. When both pipes are working together, how long does it take them to fill the tank
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An aquarium tank can hold 6600 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 55 minutes. The second pipe can fill the tank in 66 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
Given Information:
Time to fill tank by first pipe = 55 minutes
Time to fill tank by first pipe = 66 minutes
Total capacity of tank = 6600 liters
Required Information:
Time required to fill tank when both pipes are working together = ?
Answer:
Time required to fill tank when both pipes are working together = 30 mins
Step-by-step explanation:
The rate of filling the tank of the first pipe is,
first pipe = [tex]\frac{6600}{55} = 120[/tex] [tex]L/m[/tex]
The rate of filling the tank of the second pipe is,
second pipe = [tex]\frac{6600}{66}= 100[/tex] [tex]L/m[/tex]
Let x is the time to fill the tank when both pipes are used so the equation becomes,
[tex]120 + 100 = \frac{6600}{x}[/tex]
[tex]120x + 100x = 6600[/tex]
[tex]220x = 6600[/tex]
[tex]x = \frac{6600}{220}[/tex]
[tex]x = 30[/tex] [tex]mins[/tex]
Therefore, it would take 30 minutes to fill the entire tank when both pipes are used to fill the tank.
Which features describe the graph of
oth =1? Select two options.
a focus at (1040)
a focus at (0.-96)
a vertex at (-40,0)
a vertex at (0, 96)
the center at (0,0)
Answer:
4. a vertex at (0, 96) is CORRECT
5. the center at (0, 0) is CORRECT
From the given equation,
a = 40
b = 96
(h,k) = (0,0), the center
The vertices are at (0,96) and at (0, -96).
The curves open upward and downward.
c² = a² + b² = 40² + 96² = 10816
c = 104
Therefore the foci are at (0, -104) and (0, 104).
Check the given answers:
1. a focus at (104, 0) is INCORRECT
2. a focus at (0, -96) is INCORRECT
3. a vertex at (-40, 0) is INCORRECT
4. a vertex at (0, 96) is CORRECT
5. the center at (0, 0) is CORRECT
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Answer:
a vertex at (0,96)
the center at (0,0)
Step-by-step explanation:
edge
Matt and Natalie went shopping. The cost of their clothing, not including tax was $27.75. If the tax rate is 6%, estimate the total cost of their purchase. Group of answer choices
Answer:
The total cost of purchase of Matt and Natalie are $29.41
Step-by-step explanation:
We are given the following in the question:
Cost of clothing without tax = $27.75
Tax percentage = 6%
Amount of tax on clothing =
[tex]=6\%\times 27.75\\\\=\dfrac{6}{100}\times 27.75 \\\\=1.665\approx \$1.66[/tex]
Total cost of purchase =
=Total bill without tax + Amount of tax
[tex]=27.75+1.66\\=\$29.41[/tex]
Thus, the total cost of purchase of Matt and Natalie are $29.41
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day 333 people enter the park, the admission fee collected totaled $862. How many children and how many adults were admitted?
Answer:
188 children and 145 adults were admitted in the park.
Step-by-step explanation:
Given:
The admission fee at an amusement park is $1.50 for children and $4 for adults.
Total $862 collected on a certain day when 333 people enter the park.
Now, to find the children and adults admitted in the park.
Let the number of children admitted be [tex]x.[/tex]
And the the number of adults admitted be [tex]y.[/tex]
So, the total people enter the park:
[tex]x+y=333\\\\x=333-y\ \ \ ...(1)[/tex]
Thus, the total amount collected of the admission fee:
[tex]1.50(x)+4(y)=862\\\\[/tex]
Substituting the value of [tex]x[/tex] from equation (1):
[tex]1.50(333-y)+4(y)=862\\\\499.50-1.50y+4y=862\\\\499.50+2.50y=862\\\\Subtracting\ both\ sides\ by\ 499.50\ we\ get:\\\\2.50y=362.50\\\\Dividing\ both\ sides\ by\ 2.50\ we\ get:\\\\y=145.[/tex]
Thus, the number of adults = 145.
Now, to get the number of children by substituting the value of [tex]y[/tex] in equation (1) we get:
[tex]x=333-y\\\\x=333-145\\\\x=188.[/tex]
Hence, the number of children = 188.
Therefore, 188 children and 145 adults were admitted in the park.
Can random samples and proportional reasoning be used to determine precise information about a population? Explain.
Answer:
yes
Step-by-step explanation:
A population can be determined proportionally and can be used as random samples by explaining for example how much people speak a different language other than english or sampling peoples hair color,some predictions made can be true whether its asking 5,10,20,30,40,100 people.