The probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability of picking a card with an even number:
There are 10 cards on which numbers are written 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29.These cards are placed on a table with the numbers facing down.To find the probability of picking a card with an even number, first, we count all the even numbers written on the cards.12, 14, and 18 out of 10 cards there are 3 even numbers written on the cards.So, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].Therefore, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].
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COMPLETE QUESTION:
The numbers 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29 are written on separate cards, and the cards are placed on a table with the numbers facing down. The probability of picking a card with an even number is _____.
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. what does the solution of the system represent in this context? startlayout enlarged left-brace 1st row y = 35 x 2nd row y = negative 0.05 (x minus 400) squared 9,942 endlayout
The correct option is D. the number of sweatshirts for which cost and income are equal.
What is quadratic equation?Any equation that contains only one element which squares the variable and none that raises it to a higher power.
The general form form of quadratic equation is-
ax² + bx + c = 0
According to the question;
Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.
The money made by selling sweatshirts is represented by y in the systems of equations' first equation.The cost of producing x sweatshirts featuring team logos for the a professional sport league is represented by y in the second equation.Step 1: Write the following system of equations as the first step.
[tex]\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}[/tex]
Step 2: Replace the value of "y" in the equation (2).
[tex]35 x=-0.05(x-400)^{2}+9492[/tex]
Step 3: Make the equation above simpler.
[tex]35 x=-0.05 x^{2}-8000+40 x+9492[/tex]
Step 4: Write the preceding equation in generalised quadratic form.
[tex]0.05 x^{2}-5 x-1492=0[/tex]
The processes above lead to the conclusion that option D provides the proper statement.
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The complete question is-
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?
y=35x
y=-0.05(x-400)^2+9,492
A. the number of sweatshirts that generate the maximum income
B. the number of sweatshirts that generate the minimum cost
C. the number of sweatshirts for which the difference between cost and income is greatest.
D. the number of sweatshirts for which cost and income are equal
Answer:
D
Step-by-step explanation:
He said so
More than 93 percent of all blank______ are distributed as freestanding inserts in newspapers
More than 93 percent of all blank coupons are distributed as freestanding inserts in newspapers.
What is percent?
A percentage solution is a chemical or compound amount or volume per 100 mL of solution. It is a proportion of solute to solvent: X amount/100 ml = X% Percentage solutions are a simple and convenient way to record solution concentrations.A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. It is denoted by the symbol "%."To learn more about percentage visit:
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18. A8 x 6 x 4 cm³ metallic cube is melted. Find the minimum volume of molten metal which should be added to
mould it into a cube whose edge is an integer.
(1) 20
(2) 21
(3) 23
(4) 24
The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].
How to estimate the minimum volume of molten metal?Volume exists as a scalar quantity representing the amount of three-dimensional space encircled by a closed surface.
The minimum volume of a shape with measured dimensions exists provided by the lowest values of the dimensions when accounting for measurement error. Maximum Volume: The maximum volume of a shape with measured dimensions exists provided by the highest values of the measurements when accounting for measurement error.
The volume of the cube [tex]= 8*6*4[/tex]
[tex]= 192 cm^3[/tex]
To create the X as the sides of the cube we should add material.
The nearest cube number to 192 exists at 216
The amount of material to be added exists
= 216 -192
[tex]= 24 cm^3[/tex]
The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].
Therefore, the correct answer is an option (4) 24.
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Which of the following is not considered an action that would interfere with the airflow patterns at the front opening of the biosafety cabinet
An action that would not interfere with the airflow patterns at the front opening of the biosafety cabinet is a researcher discarding waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening.
What is biosafety?It should be noted that biosafety simply means the use of safety equipment as specifically designs tools to ensure that people are protected from hazards.
In this case, when a researcher discards waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening, it won't interfere with the airflow pattern.
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Desiree opens an account with one deposit of $6500. she receives a statement twice a year, just after the interest is applied. which type of account is desiree most likely using?
From Longman Dictionary of Contemporary English opens an account to start an account at a bank or other financial organization by putting money into it Mary was in the bank to ask about opening a current account.
Step 1: Visit the official website of the bank in which you wish to open an account. Step 2: Fill in the application form online along with a digital copy of address proof, identity proof, age proof, income/employment proof, and photographs.
You need to be at least 18 years old to open an account. However, you can open a joint account as a minor with a parent or legal guardian as an account co-owner. Some banks do offer accounts tailored for minors.
Please check the attached file for a complete answer.
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Find the equation of the line with slope = 6 and passing through (2,20). write your equation in the form y = mx + b.
Answer:
y = 6x + 8
Step-by-step explanation:
y = mx + b
20 = 6(2) + b
b = 8
y = 6x + 8
Instructions: Find the length of the missing sides. Round your
answers to the nearest tenth. (Hint: Always make sure to label
your triangle first with your reference angle)
Degree 54
Hypotenuse 24
How do i find x and y?
The values of x and y are 19 and 14 respectively.
How to determine the lengthGiven the hypotenuse = 24
Opposite = x
Adjacent = y
Let's use the sine ratio to find the opposite side
sin of angle = opposite/hypotenuse
sin 54 = x/24
Cross multiplysin 54 × 24 ,= x
x = 19.42
x = 19
To find the adjacent side, we use cosine ratio
cos = adjacent/hypotenuse
cos 54 = y/25
Cross multiply
cos 54 × 24 = y
y = 14
Thus, the values of x and y are 19 and 14 respectively.
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Mari works part time selling both hats and scarfs. One week she earns $114.00 by selling eight hats and 10 scarves. The following week she sold 12 hats and six scarves and earned $108.00. How much does she earn for each hat and scarf she sells?
Using a system of equations, it is found that she earns $5.5 for each hat and $7 for each scarf sold.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Cost of a hat.Variable y: Cost of a scarf.One week she earns $114.00 by selling eight hats and 10 scarves, hence:
8x + 10y = 114.
The following week she sold 12 hats and six scarves and earned $108.00, hence:
12x + 6y = 108
Simplifying by 6:
2x + y = 18
y = 18 - 2x.
Replacing in the first equation:
8x + 10y = 114.
8x + 10(18 - 2x) = 114
12x = 66
x = 66/12
x = 5.5
y = 18 - 2x = 18 - 2 x 5.5 = 7.
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A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 29 ft long and 20 ft wide.
Find the area of the garden. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
15.7 square feet
Step-by-step explanation:
To find the area of the garden we find the area of the rectangle and the area of the semicircle.
The area of the rectangle:
A=bh
A=(29)(20)
A=580ft^2
As shown in the picture, the width of the rectangle is 20 ft wide, which means that the diameter of the semicircle is also 20ft wide. The diameter is two times the radius, which means the radius of the semicircle is 10ft.
The area of a circle is represented by the equation: [tex]A=\pi r^{2}[/tex]
A semicircle is half of a circle, therefore the equation to find the area of a semicircle is: [tex]A=\frac{1}{2}\pi r^{2}[/tex]
Plugging our radius of 10ft in we get:
[tex]A=\frac{1}{2}\pi (10)\\ A=5\pi[/tex]
We use 3.14 for our value of [tex]\pi[/tex] to get:
[tex]A=5(3.14)\\A=15.7ft^{2}[/tex]
Therefore, the area of the rose garden is 15.7 square feet.
use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4
The expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.
The power-reducing formula, for cosine, is,
cos² θ = (1/2)[1 + cos 2θ].
In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.
We can do it as follows:
cos⁴ θ
= (cos² θ)²
= {(1/2)[1 + cos 2θ]}²
= (1/4)[1 + cos 2θ]²
= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}
= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)
= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]
= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8
= 3/8 + cos 2θ/4 + cos 4θ/8
= [ 3 + 2cos 2θ + cos 4θ]/8.
Thus, the expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.
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Can someone help me out on this please having trouble on both and show work please !!
The difference of the expression is as follows:
(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12
3(x - 5) - (2x + 4) = x - 19
How to find the difference of the expression?The difference of the expression can be found when we combine the like terms.
Therefore,
(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)
6y⁴ + 3y² - 7 - 12y⁴ + y² - 5
6y⁴ - 12y⁴ + 3y² + y² - 7 - 5
- 6y⁴ + 4y² - 12
3(x - 5) - (2x + 4)
3x - 15 - 2x - 4
3x - 2x - 15 - 4
x - 19
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Help me solve this question!
Answer:
1st quartile is 136
The second quartile is also the median 142
The third quartile is 162
The interquartile range is the difference between the 3rd and first quartile or 26
Step-by-step explanation:
Write an equation of the line that passes through the point (8, 1) with slope 5. A. y - 1 = 5(x − 8) B. y − 1 = - -5(x − 8) - C. y - 8 = -5(x - 1) OD. y - 8 = 5(x − 1) Question Progress
Answer:
[tex]y-1=5(x-8)[/tex]
what are the solutions to 5x^2 - x - 1 < 0
I SHOULD ALREADY KNOW THIS
[tex]t \geqslant 35[/tex]
Since there are at least 35 tic tacs, there has to be 35 tic tacs or more in the box.m
A math teacher gives a quiz. Each question on the quiz is
worth 8 points. A score of 75 is a passing grade.
Which number of correct answers will result in a passing
grade?
From statement equation, the number of correct answers will result in a passing grade is 9.3
What number of questions is required for passing grade ?Given that each question on the quiz is worth 8 points.
Also given a score of 75 is a passing grade.
Let the number of correct answered questions be x
Thus the total score of the correct answers is 8x
The statement equation is -
⇒ 8x = 75
⇒ x = 75/8 = 9.3
∴ x ≈ 9
Therefore, from statement equation, the number of correct answers will result in a passing grade is 9.3
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Dion is 4 years older than Agustina. In 3 years the sum of their ages will be 46. How old is Dion now?
Answer:
22
Step-by-step explanation:
Dion (d) is 4 years older than Agustina (a)
d=a+4
In 3 years the sum of their ages will be 46
d+3+a+3=46
d+a+6=46
d+a=40
d=40-a
d=a+4
a+4=40-a
2a=36
a=18
Plug a back in
18+4=d
22=d
d=22
Sorry if this was a little long.
simplify 16-4(3x-2)²
16-4(3x-2)²
=16-4(3x-2)(3x-2)
=16+−36x²+48x+−16
=(−36x²)+(48x)+(16+−16)
=−36x²+48x
Answer:
[tex] \red{- 12x(3x - 4)}[/tex]
Step-by-step explanation:
We know that,
[tex](a - b)^{2} = {a}^{2} - 2ab + {b}^{2} \\ [/tex]
Accordingly, let us solve the sum now.
[tex]16 - 4(3x - 2)^{2} \\ 16 - 4(9 {x}^{2} - 12x + 4) \\ 16 - 36 {x}^{2} + 48x - 16 \\ - 36 {x}^{2} + 48x \\ - 12x(3x - 4)[/tex]
Can someone please help
Solving the given equation, the value of v that makes the statement true is:
A. v = 8.
What is the given equation?The equation is:
[tex]12 = 12 + \frac{v - 8}{2}[/tex]
Hence:
[tex]\frac{v - 8}{2} = 0[/tex]
Applying cross multiplication:
v - 8 = 0
v = 8.
Hence option A is correct.
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Please answer questions three to five!
The computation shows that the amount that will be charged will be $5.00 and $9.00 respectively.
How to illustrate the information?When the customer has a 6 pound Chihuahua, the amount that will be charged will be $5.00.
When a customer has a 65 pound Labrador, the amount that will be charged is $9.00.
This is illustrated as the cost is based on the weights given.
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BRAINLIEST TO CORRECT ANSWER
There is a pair of parallel sides in the following shape.
what is the area
The area of the given figure is 38 square units
Area of a trapezoidThe area of the given trapezoid is expressed as:
A = 0.5(a+b)h
where
a and b are the sides
h is the height
Substitute
A = 0.5(9+10) * 4
A = 19 * 2
A = 38 square units
Hence the area of the given figure is 38 square units
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Write the equation for a parabola with a focus at (7,2) and a directrix at y = -2 y = ?
Equation of the parabola is [tex]y=\frac{1}{8} (x-7)^2[/tex] with a focus at [tex](7,2)[/tex] and a directrix at [tex]y=-2[/tex]
How to find the equation of parabola with focus and directrix ?
We know that focus of the parabola [tex](h,k+p)=(7,2)[/tex]
So [tex]k+p=2[/tex]......(a)
And directrix of the parabola
[tex]y=k-p\\=-2[/tex]
[tex]k-p=-2[/tex]........(b)
So add the equation (a) AND (b)
[tex]k+p=2\\k-p=-2\\------------\\2k=0\\k=0\\p=2[/tex]
Equation of the parabola with directrix and focus
[tex]y-k=\frac{1}{4p} (x-h)^2[/tex]
Substitute all the values
[tex]y-0=\frac{1}{4(2)} (x-7)^2\\y=\frac{1}{8} (x-7)^2[/tex]
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Simplify:6 to the power of 5/6to the power of 2.
A.1/6 to the power of 3
B.6 ttpo 7
C.6ttpo 2
D.6ttpo 3
The value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
How to simplify the expression?The expression is given as:
6 to the power of 5/6to the power of 2.
Rewrite properly as:
6^5/6^2
Apply the law of indices
6^(5-2)
Evaluate the difference
6^3
Hence, the value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
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David is currently 3 times as old as his son. If David’s son’s current age is x years, how old will David be after 3 years?
Dave is 18 years old.
What is algebraic expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11
Given
Let x be Dave’s age today. Then:
x=3(x+3)-3(x-3)
x=3x+9–3x+9
x=18
Dave is 18 years old.
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find the value of x for which the fraction 4x +9/7x
Answer:
x = 3
Step-by-step explanation:
Here ,
4x + 9 =7x
--> 4x - 7x = -9
--> -3x = -9
--> ≠ x = -9/3
--> x = 3
Meg plotted the graph below to show the relationship between the temperature of her city and the number of sweaters sold at a store:
Part A: In your own words, describe the relationship between the temperature of the city and the sale of sweaters in the city. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
PLEASE HELP WITH PART B ASAP
The explanation about the graph is illustrated below.
How to illustrate the graph?The graph shows 0 to 30 on the x-axis at increments of 5 and 0 to 12 on the y-axis at increments of 1. The label on the x-axis is Temperature in degrees C, and the label on the y axis is the Number of Sweaters Sold.
If you will draw lines through, (12.5,6) and (15,4), it will best represent a line of best fit, because most of the points on the same and opposite sides of line are equidistant from each other.
Equation of line passing through (12.5,6) and (15,4) A line of best is the line that passes through all or some points or only through a single point, which describes the relationship between x and y values of data set
4x + 5y = 80
5y = -4x + 80.
y = -4x/5 + 16
Slope = -4/5 and y intercept is 16.
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Hat is the area of the shaded face of the cylinder is 22m give your answer to the nearest whole number and give the correct units
The area of the shaded face of the cylinder is 1,520 mm².
How to find the area of the shaded area?We can see that the shaded area of the cylinder is circular in shape.
This means that we can find the area of the shaded area by finding the area of the circle.
The radius of the circle is given as 22 mm.
The formula for finding the area of a circle is given as:
Area = πr²
= 3.14 × 22 × 22
= 1,519.76
≈ 1520 mm²
Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².
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Disclaimer: The question was incomplete, the complete question is attached below.
an economic research commission claimed that among the 500 stores there are 308 dealing with european companies, 266 dealing with asian companies 103 dealing with both sides regularly and 59 not dealing with either side. i) what is the probability that the stores deal with european or asian companies? ii) what is the probability that the stores do not deal with european companies? iii) what is the probability that the stores only deal with asian companies? iv) what is the probability that stores do not deal with only one type of company
Step-by-step explanation:
Let S be the set of all the stores in the sample, A be the set of stores dealing with Asian companies and E but the set of stores dealing with European companies
i. The set of stores that deal with European or Asian companies is A ∪ E. The inclusion-exclusion principle states that |A ∪ E| = |A| + |E| - |A ∩ E| = 266 + 308 - 103 = 471. So P(A ∪ E) = 471/500 = 0.942
ii. E' = S - E. |S-E| = 500 - 308 = 192. So P(E') = 192/500 = 0.384
iii. |A - E| = |A| - |A ∩ E| = 266 - 103 = 163. So P(A - E) = 163/500 = 0.326
iv. Stores that do not deal with only one type of company, must deal with both Asian and European companies. We are given that |A ∩ E| = 103. So P(A ∩ E) = 103/500 = 0.206
Easy, right?
Then mark as brainlist!
The movement of the progress bar may be uneven because questions can be worth more or less
(including zero) depending on your answer.
What are the exponent and coefficient of the expression 46-³?
The exponent is 3 and the coefficient is -4.
The exponent is -3 and the coefficient is 4.
O
The exponent is -3 and the coefficient is -4.
The exponent is 4 and the coefficient is -3.
Determine the measure of the indicated angle in the following triangle:
Answer:
Θ ≈ 58°
Step-by-step explanation:
using the Cosine Rule in the triangle
cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )