Answer:
Therefore the probability that a pen from the first box and a crayon from the second box are selected is [tex]\frac5{16}[/tex]
Step-by-step explanation:
Probability:
The ratio of the number of favorable outcomes to the number all possible outcomes of the event.
[tex]Probability=\frac{\textrm{The number favorable outcomes}}{\textrm{The number all possible}}[/tex]
Given that,
Three plain pencils and 5 pens are contained by the first box.
Total number of pens and pencils is =(3+5)=8
The probability that a pen is selected from the first box is
=P(A)
[tex]=\frac{\textrm{The number pens}}{\textrm{Total number of pens and pencils}}[/tex]
[tex]=\frac{5}{8}[/tex]
A second box contains three colored pencils and three crayons.
Total number of pencils and crayons is =(3+3)=6
The probability that a crayon is selected from the second box is
=P(B)
[tex]=\frac{\textrm{The number of crayon}}{\textrm{Total number of crayons and pencils}}[/tex]
[tex]=\frac{3}{6}[/tex]
Since both events are mutually independent.
The required probability is multiple of the events
Therefore the required probability is
[tex]=\frac58\times \frac36[/tex]
[tex]=\frac5{16}[/tex]
Kiyoshi's phone plan costs $17.50 per month plus $0.15 per text message. What is the maximum number of text messages Kiyoshi can use so the phone bill is no more than $56.50?
Answer:
260 text
Step-by-step explanation:
First you're gonna want to subtract 17.50 form 56.50 and get 39.00 left over for text messages.
dividing 39 by .15 ([tex]\frac{39}{0.15}[/tex]) gives you 260
he can send 260 text per billing period
Answer:
She can sen a MAXIMUM of 260 texts
Step-by-step explanation
so lets start with the info we know
Her limit - $56.50
a flat rate (constant) - $17.50
and how much is cost PER text - $0.15
so we can make an inequality
56.50 ≤ .15x + 17.50
first, we would take away the constant
56.50-17.50 = 39
39 ≤ .15x
divide by .15
39/.15
leaving us with
260≤ X
Which of the following statements are true about a reflection? Select all that apply.
Answer:
where are your answers?
I need all the question to answer becbecause it seems it is incomplète.
Step-by-step explanation:
however, Reflection in algèbre is something that changes place or position but it never changes its size. for example you can flippe a triangle's position and it will remind the same but it just changes place or position .
I hope this helps .
Answer:
A B E
Step-by-step explanation:
g(x) = x^3 - 5; Find g(5)
Answer:
g(5) = 120
Step-by-step explanation:
g(x) = x^3 - 5;
Let x=5
g(5) = 5^3 -5
= 125 -5
= 120
Answer:
g(5) = 120
Step-by-step explanation:
We want to find g(x) when x is equal to 5, so we can substitute 5 in for x.
g(x) = x^3 - 5
g(5) = 5^3 - 5
Solve the exponent
g(5) = 125-5
Subtract
g(5) = 120
What is 4/4 as a decimal
Answer: the answer is 1.00
Step-by-step explanation: 4/4 as a decimal is 1.00 because if you have four parts out of 4 then it makes a whole so it is 1.00
a
The solution is 1.00
The value of the equation is A = 1.00
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number be represented as n
The value of n = ( 4/4 )
A = ( 4/4 ) be equation (1)
On simplifying the equation , we get
The value of A = 1
The value of A in decimal form is A = 1.00
Therefore , the value of A is 1.00
Hence , the value of the equation is A = 1.00
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Circle O has an area of 200m^2. Point A and B lie on the circle. Sector AOB has an area of 50m^2. What is the measure of angle AOB?
90
25
45
180
Write a quadratic function whose graph has a vertex of (3, 2) and passes through the point (4, 7), using f(x) = a(x - h)^2 + k (vertex form).
THANK YOU FOR HELPING!!!
The quadratic function is f(x) = 5(x - 3)² + 2.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
where (h, k) is the vertex of the parabola.
We are given that the vertex is (3, 2), so we have:
h = 3
k = 2
We also know that the parabola passes through the point (4, 7).
We can use this point to find the value of a:
7 = a(4 - 3)² + 2
5 = a
Therefore, the quadratic function is:
f(x) = 5(x - 3)² + 2
This quadratic function has a vertex of (3, 2) and passes through the point (4, 7).
Thus,
The quadratic function is f(x) = 5(x - 3)² + 2.
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Someone please answer this will mark brainliest
Answer:
The answer to your question is the letter B.
Step-by-step explanation:
Data
√3/2 -2π 4/5 -6.5 7 2/3
Process
1.- Get the decimal values of each data
√3/ 2= 0.87 -2π = -6.28 4/5 = 0.2 -6.5 = -6.5 7 2/3 = 7.67
2.- Order the numbers from greatest to least
7.67 > 0.87 > 0.2 > -6.28 > -6.5
or 7 2/3 > √3/2 > 4/5 > -2π > -6.5
3.- Conclusion
The right answer is B.
Edith needs 65 yards of yarn to knit a baby hat and 580 yards of yarn to knit a baby blanket. A ball of yarn contains 420 feet of yarn. How many balls of yarn does Edith need to buy to make the baby hat and baby blanket?
Answer:
5
Step-by-step explanation:
There are 3 feet in a yard, so 420 feet is 420/3 = 140 yards.
The total number of yards Edith needs is ...
65 yd + 580 yd = 645 yd
So, the total number of balls of yarn Edith needs is ...
(645 yd)/(140 yd/ball) ≈ 4.61 balls
Edith needs to buy 5 balls of yarn to make her projects.
What's the volume of the cone? Round to tenths place please.
Given:
Given that the radius of the cone is 2 inches.
The height of the cone is 4 inches.
We need to determine the volume of the cone.
Volume of the cone:
The volume of the cone can be determined using the formula,
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
where r is the radius of the cone and h is the height of the cone.
Substituting r = 2 and h = 4 in the above formula, we get;
[tex]V=\frac{1}{3} (3.14) (2)^2 (4)[/tex]
[tex]V=\frac{1}{3} (3.14) (4) (4)[/tex]
[tex]V=\frac{1}{3}(50.24)[/tex]
[tex]V=16.75[/tex]
Thus, the volume of the cone is 16.75 cubic inches.
What’s the slope of (8,10) (-7,14)
Using the formula for slope, we calculated that the slope of the line passing through the points (8,10) and (-7,14) is -4/15.
Explanation:The slope of a line between two points ((x1,y1) and (x2,y2)) can be calculated using the formula for slope: m = (y2 - y1) / (x2 - x1).
In this case, your two points are (8,10) and (-7,14).
Therefore, we can calculate the slope using these points:
m = (14 - 10) / (-7 - 8) = 4/-15 = -4/15.
So, the slope of the line passing through the given points is -4/15.
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Based on the Nielsen ratings, the local CBS affiliate claims its 10 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the null hypothesis
Answer:
H0:p=0.41
Step-by-step explanation:
The null hypothesis always contain equality i.e. (=) sign. The null hypothesis contains the statement regarding population parameter. Here, the claim about population proportion is mentioned in the statement that 10 p.m. newscast of local CBS reaches 41% of viewers. So, the null hypothesis would be
Null hypothesis:H0: p=0.41.
Three runners — Andy, Blaise, and Susie — were competing in a 100-meter race. When Andy reached the finish line, Blaise was 10 meters behind him. When Blaise reached the finish line, Susie was 10 meters behind her. At the moment that Andy reached the finish line, Susie was how many meters behind him? Keep working and you will earn half credit for correctly solved problem.
Final answer:
Susie was 20 meters behind Andy when he reached the finish line in the 100-meter race.
Explanation:
To determine how many meters Susie was behind Andy at the moment Andy reached the finish line during the 100-meter race, let's consider the information given:
Andy finished the race.
Blaise was 10 meters behind Andy at that moment.
Susie was 10 meters behind Blaise when Blaise finished the race.
When Blaise reached the finish line, Andy would have already finished since Blaise was behind by 10 meters. However, at the moment Andy finished, Susie was also behind Blaise, who was 10 meters from finishing. Hence, Susie was 10 meters (the distance Blaise was behind Andy) + 10 meters (the distance Susie was behind Blaise at her finish) = 20 meters behind Andy when he finished the race.
In conclusion, Susie was 20 meters behind Andy when Andy reached the finish line.
Olivia is cutting a 1 \dfrac12 \text{ m}1 2 1 m1, start fraction, 1, divided by, 2, end fraction, start text, space, m, end text by \dfrac34\text{ m} 4 3 mstart fraction, 3, divided by, 4, end fraction, start text, space, m, end text piece of rectangular paper into two pieces along its diagonal. Find the area of each of the pieces.
Answer: 9/6 metre
Step-by-step explanation:
From the question, Olivia is cutting a 1 1/2m by 3/4m piece of rectangular paper into two pieces along its diagonal
This will result into two congruent triangular pieces.
Let us first find the area of each piece by finding the area of the original rectangle and dividing it by two.
The area of a rectangle is given by multiplying the length and the width:
1 1/2 × 3/4
We can change the first fraction to an improper fraction:
(1×2)+1 = 2+1 = 3; this gives us 3/2:
3/2 × 3/4 = 9/8 = 1 1/8
The area of the entire rectangle is 1 1/8 sq. m., or 1.125 sq. m.
Divide this by 2:
9/8 ÷ 2
9/8 × 1/2 = 9/16
The area of each rectangle is 9/16 sq. m., or 0.5625 sq.
Answer:
9/16
Step-by-step explanation:
What is the value of x?
What is the measure of XVY? XVY=
Tristan has some dimes and some quarters. He has at least 20 coins worth at most $4.25 combined. If Tristan has 10 dimes, determine the maximum number of quarters that he could have. If there are no possible solutions, submit an empty answer.
Answer:
The maximum number of quarters that he could have is 13
Step-by-step explanation:
Let x represent the number of quarters he could have. If he has 10 dimes and has at least 20 coins, then
→ x + 10 >= 20
→ x >= 10 (1)
His coins worth at most $4.25. Also, it is known that 1 dollar is equal to 100 cents, 1 dime is equal to 10 cents and 1 quarter is equal to 25 cents.
→ (x * 25) + (10 * 10) <= (4.25 * 100)
→ 25x + 100 <= 425
→ 25x <= 325
→ x <= 13 (2)
If we combine the equation 1 and 2:
10 <= x <= 13
The maximum value of x is 13
PreCalc help with sums. I will mark brainliest. (also can you explain WHY you got what answer you got? Thanks)
Answer:
1) first two (A & B)
2. -1,533
Step-by-step explanation:
Sum to infinity is finite when
-1 < r < 1
Option 1: r = -¼
Option 2: r = 27/81 = ⅓
Option 3: r = 3/2
Option 4: r = 17.75/7.1 = 2.5
a = -3
r = -6/-3 = 2
S9 = -3 × (2⁹ - 1)/(2 - 1)
= -1533
Maura can buy daffodil bulbs in packages of 3 for $5.37 or in packages of 2 for $4.52. How much money does she save by buying 30 bulbs at the better price?
Answer:
$14.10
Step-by-step explanation:
To have 30 bulbs, Maura can buy 10 packages of 3 at $5.37 each, for a total of $53.70. Or, she can buy 15 packages of 2 at $4.52 each, for a total of $67.80.
Buying in packages of 3, Maura saves $67.80 -53.70 = $14.10.
Explain why a cross section of a polyhedron does not always match the base of that polyhedron.
Explanation:
A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.
If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.
For example, the cross sections of a cube include ...
triangle, square, rectangle, trapezoid, general quadrilateral, pentagon, hexagon
Answer: A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.
If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.
Step-by-step explanation.
A team competes in 40 matches. Of those matches, he wins 16. What percent of the matches did the team win?
Answer:
6.4%
Step-by-step explanation:
Answer:
6.4%
Step-by-step explanation:
Solving Square Root Worksheet (x - k)^2 Part 2
4. 3(x - 2)^2 = 40
5. -2(x - 1)^2 = 36
6. 4(x - 1)^2 = 8
Answer:
4. x = 2 + 2sqrt(10/3), 2- 2sqrt(10/3)
5. No real solutions
x = 1 + 3sqrt(2) i, 1 - 3sqrt(2) i,
6. x = 1 + sqrt(2), 1 - sqrt(2)
Step-by-step explanation:
4. 3(x - 2)² = 40
(x - 2)² = 40/3
(x - 2) = +/- sqrt(40/3)
x - 2 = +/- 2sqrt(10/3)
x = 2 +/- 2sqrt(10/3)
5. -2(x - 1)² = 36
(x - 1)² = -18
A perfect square can never be negative for real values of x
(x - 1) = +/- i × sqrt(18)
x - 1 = +/- i × 3sqrt(2)
x = 1 +/- i × 3sqrt(2)
6. 4(x - 1)² = 8
(x - 1)² = 2
x - 1 = +/- sqrt(2)
x = 1 +/- sqrt(2)
Suppose you put $1000 in an account earning 5.5% interest compounded continuously. How much will be in the account after four years?
a. $941
b. $1,246
c. $1,057
d. $1,839
Answer: The correct answer will be $1,220 in the account after four years.
Step-by-step explanation: For this problem we will use the "Simple Interest" equation to find the amount of interest you will earn after 4 years.
First, convert 5.5% to a decimal, 0.055.
I, interest = 1000 x 0.055 x 4
I = $220
Now add the interest to the total amount of money originally in the account.
1000 + 220 = $1,220
Final answer:
The amount in the account after four years, with continuous compound interest at a rate of 5.5%, is approximately $1246. Therefore, after four years, the amount in the account will be closest to option (b) $1,246.
Explanation:
To calculate the amount in the account after four years, we can use the formula for continuous compound interest: A = P [tex]e^{(rt)}[/tex], where A is the final amount, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, P = $1000, r = 5.5% = 0.055, and t = 4. Plugging these values into the formula, we have:
A = $1000 × [tex]e^{(0.055 \times 4)}[/tex]
A = $1000 × [tex]e^{0.22[/tex]
A ≈ $1000 × 1.246
Therefore, the amount in the account after four years is approximately $1246.
work out the area of triangle give your answer to 1 decimal place
Given:
Given that the triangle.
Let the length of the side a be 10 cm.
Let the length of the side b be 13 cm.
Let the measure of ∠C is 105°
We need to determine the area of the triangle.
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]A=\frac{1}{2} a b \ sin \ c[/tex]
Substituting a = 10, b = 13 and ∠C = 105°, we get;
[tex]A=\frac{1}{2}(10)(13) \ sin \ 105[/tex]
Simplifying, we get;
[tex]A=\frac{1}{2}(10)(13)(0.966)[/tex]
[tex]A=\frac{1}{2}(125.58)[/tex]
[tex]A=62.79 \ cm^2[/tex]
Rounding off to 1 decimal place, we have;
[tex]A=62.8 \ cm^2[/tex]
Thus, the area of the triangle is 62.8 cm²
The area of the triangle is 65 square centimeters when rounded to one decimal place.
To find the area of a triangle, you can use the formula:
[tex]Area = (\frac{1}{2} ) \times base \times height[/tex]
In this case, you have a base of 13 cm and a height of 10 cm. Plug these values into the formula:
[tex]Area =(\frac{1}{2} ) \times 13 cm \times 10 cm[/tex]
[tex]Area = (\frac{1}{2}) \times 130 cm^2[/tex]
Now, calculate the area:
[tex]Area = 65 cm^2[/tex]
So, the area of the triangle is 65 square centimeters when rounded to one decimal place.
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a box used for shipping a volleyball set measures 10 inches by 20 inches by 40 inches. what is the longest length of support pole that will fit into the box, rounded to a tenth of an inch?
Answer:
45.8 inches
Step-by-step explanation:
Considering the given dimensions and taking 40 inches for length, 20 inches for height and 10 inches for width. The diagonal that runs from bottom to top of box will give the longest possible length of a pole.
Diagonal at the bottom of box
Diagonal=√(l²+w²)
Where l and w represent length and width respectively
Diagonal=√(40²+10²)=√1700
Diagonal between the height and bottom diagonal
Longest diagonal=√(20²+√1700)=√2100=45.8257569495584
Rounded off, the diagonal is approximately 45.8 inches
The longest length of a support pole that will fit into the box measures approximately 45.8 inches.
Explanation:To find the longest length of a support pole that will fit into the box, we need to determine the length of the diagonal of the box. The diagonal length can be found using the formula:
diagonal = √(length^2 + width^2 + height^2)
Substituting the given values:
diagonal = √(10^2 + 20^2 + 40^2) = √(100 + 400 + 1600) = √2100 ≈ 45.82 inches.
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Ann wants to wallpaper the back wall of her bedroom. The wall is in the shape of a rectangle. Its length is 17 feet and its width is 13 feet. Suppose wallpaper costs $5 for each square foot. How much will wallpaper cost for the wall?
Answer:
The wallpaper would cost 1105 $
Which is a y-intercept of the continuous function in the table? (5, 0) (0, 1) (0, 5) (1, 0)
The possible y-intercepts for the given continuous function from the table are (0,1) and (0,5).
Explanation:In this mathematical problem, the student is asking about the y-intercept of a function represented in a table. The y-intercept of a continuous function is a point where the line of the function intersects or touches the y-axis on a graph. This point is always (0, y). If we look at the given points, only (0,1) and (0,5) can potentially be y-intercepts because they have 0 as their x-coordinate, which is the requirement for a point to be a y-intercept.
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y=4x-9 what’s the missing value in the solution to the equation?
Answer:
x=2.25
Step-by-step explanation:
Let's break this down:
Saying "y=", is just like saying "0=", so we can say that;
0=4x-9
We need to isolate the variable, and to do that we should add 9 to both sides and cancel it out.
9=4x
Now we need to eliminate the coefficient by dividing both sides by four
[tex]9/4=4x/4[/tex]
Which cancels out four, giving us
2.25=x
Hope this helps and please correct me if I am wrong:)
<3
Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 160 workers can produce 32 cars in 2 hours, find the number of cars that 220 workers can produce in 3 hours.
Answer:
They'll build 66 cars in those conditions.
Step-by-step explanation:
In this case we can use a compounded rule of three to solve the problem. We need to set it up as shown bellow:
160 workers -> 32 cars -> 2 hours
220 workers -> x cars -> 3 hours
If the number of workers rise, then we expect the number of cars to rise aswel, so they're directly proportional. If the number of hours worked increase we can expect the number of cars to increase aswell, so they're directly proportional. We can now set the fractions:
(160*2)/(220*3) = 32/x
320/660 = 32/x
x = (32*660/320) = 66 cars
They'll build 66 cars in those conditions.
Final answer:
To find the number of cars that 220 workers can produce in 3 hours, we can use the joint variation equation and the given information. By solving for the constant of variation, we can substitute the new values to find the answer.
Explanation:
To solve this problem, we can set up a joint variation equation:
cars = k * workers * time
Given that 160 workers can produce 32 cars in 2 hours, we can substitute these values into the equation:
32 = k * 160 * 2
Solving for k, we find that k = 0.1.
Now, we can use this value of k to find the number of cars that 220 workers can produce in 3 hours:
cars = 0.1 * 220 * 3
cars = 66
Therefore, 220 workers can produce 66 cars in 3 hours.
If the equation f(x) = 3x + 5 represents the cost of buying T-Shirts on Amazon.com;
evaluate the equation for f(13).
Answer:
f(13) = 44
Step-by-step explanation:
f(13) = 3 (13) +5 = 39 + 5= 44
(08.03)
Solve the system of equations and choose the correct answer from the list of options. (4 points)
x-y=7
y = 3x + 12
Answer:
rearrange them properly to get
x-y=7
-3x+y=12
( by elimination method)
x-y = 7
-3x+y=
(x+ –3x) + (–y+y) = (7+12)
-2x+0= 19
x= -9.5
from eqn(i)
x-y=7
-9.5 - y=7
-y=16.5
y= -16.5
What is the approximate value of irrational number e (round to 5 decimal places)?
Answer:
2.71828
Step-by-step explanation:
In this question, we are asked to give the approximate value of the irrational number e.
We should understand that just like Pi, which is the ratio of the circumference of a circle to the diameter, we have the number called e. It is also a consistent like Pi and has an approximate value of 2.71828.
What does it mean when it is called irrational? it is an irrational number because it doesn’t have an exact fraction which is the ratio of two numbers and thus it has a non-ending list of numbers after the decimal point.
Final answer:
The irrational number e, also known as Euler's number, is approximately 2.71828 when rounded to five decimal places. It is crucial in mathematics, particularly calculus.
Explanation:
The question asks for the approximate value of the irrational number e rounded to five decimal places. The number e is a fundamental constant in mathematics, often referred to as Euler's number, which is approximately equal to 2.71828 when rounded to five decimal places.
This number plays a crucial role in various branches of mathematics, especially in calculus, relating to the rate of growth or decay in natural phenomena.