Answer:
[tex]\frac{1}{15}[/tex]
Step-by-step explanation:
In probability,
"AND" means "multiplication"
"OR" means "ADDITION"
We want probability of Blue Pen and Yellow Highlighter. So we find individual probabilities and "MULTIPLY" them.
Let P(b) be probability of blue pen
Let P(y) be probability of yellow highlighter
We know probability of event is that event divided by total number of that
So,
There are 4 + 2 = 6 pens
Blue pen = 2
Hence,
P(b) = 2/6 = 1/3
And,
There are 5 highlighters
Yellow highlighter = 1
Hence,
P(y) = 1/5
Now,
P(b and y) = 1/3 * 1/5 = 1/15
Hence,
probability of grabbing blue pen and a yellow highlighter is [tex]\frac{1}{15}[/tex]
Answer:
2/15
Step-by-step explanation:
210000000 in standard form
Answer:
2.1 x 10^8
Step-by-step explanation:
2.1*10^8
The first number can not exceed ten so just count how many decimal place it would be and that should be the power.
The volume of one cube is 1/216 times the volume of the second cube. How many more times
is the length measurement of the second cube?
A 21 times
B 16 times
C 6 times
D 4 times
Answer:
c 6 times that the answer
Final answer:
The second cube's side length is 6 times that of the first cube because the volume of a cube is a cubic function of its side length, and taking the cube root of 1/216 gives us 1/6.
Explanation:
The student's question is asking to determine how many times larger the side length of the second cube is compared to the first cube, given that the volume of the first cube is 1⁄216 times the volume of the second cube. The volume of a cube is calculated by raising the side length to the third power (V = s3). Therefore, if we denote the side length of the first cube as s and that of the second cube as S, we have s3 = 1⁄216S3. To find the side length ratio, we take the cube root on both sides of the equation, yielding s = 1⁄6S, which means the second cube's side length is 6 times that of the first cube.
The correct answer to the question is C, 6 times
Which of the following are roots of the polynomial function?
Check all that apply.
(x) = x2 - 6x + 7x-2
Answer:
x=1, -2
Step-by-step explanation:
x^2-6x+7x-2
x^2+x-2
factor out the trinomial,
(x-1)(x+2)
zero property
x-1=0, x+2=0,
x=0+1=1
x=0-2=-2
5 3⁄10 hectometers = meters
Answer:
[tex]\large\boxed{5\dfrac{3}{10}\ hectometers=530\ meters}[/tex]
Step-by-step explanation:
[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]
[tex]5\dfrac{3}{10}=5.3\\\\1\ hectometers=100\ meters\qquad(1\ hm=100m)\\\\5\dfrac{3}{10}\ hm=5.3\ hm=5.3\cdot100\ m=530\ m[/tex]
Write and solve 7 less than the product of 4 and 6
Answer:
7<24
Step-by-step explanation:
I'm bad at explaining but I hope this helps if I'm actually right
7<4×6
7<24
The required inequality for 7 less than the product of 4 and 6 is 7 < 24.
Equality is determined for statement 7 less than the product of 4 and 6.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
The statement states that 7 is less than the product of 6 and 4
Now,
the product of 6 and 4 = 6 * 4 = 24, Implies
7 < 24
Thus, the required inequality for 7 less than the product of 4 and 6 is 7 < 24.
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A rectangle is 19 feet long and 42 feet wide. What is the area of the rectangle, in square yards? Express your answer as a mixed number in lowest terms.
Answer:
[tex]86\frac{2}{3}[/tex] yards²
Step-by-step explanation:
19 feet = [tex]\frac{19}{3}[/tex] yards
42 feet = 14 yards
14 × [tex]\frac{19}{3}[/tex] = [tex]\frac{266}{3}[/tex] = [tex]86\frac{2}{3}[/tex]
What does control for eximerment mean
.
Answer:
The definition of a control experiment is a test where the person conducting the test only changes one variable at a time in order to isolate the results. An experiment where all subjects involved in the experiment are treated exactly the same except for one deviation is an example of a control experiment.
Step-by-step explanation:
Answer/Explanation:
You need a control to show how 1 changed variable will change to result.
45.6379 rounded to the nearest hundread
Answer:
45.64
Step-by-step explanation:
thats the answer
To round 45.6379 to the nearest hundred, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros.
Explanation:To round 45.6379 to the nearest hundred, we look at the digit in the hundredth place, which is 5. Since 5 is greater than or equal to 5, we round up. Therefore, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros. The rounded number to the nearest hundred is 45.6400.
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Leon’s older brother is 4 3/4 feet tall . Leon is 1/3 foot shorter than his brother . How tall is Leon ?
Answer:
4 5/12
Step-by-step explanation:
4 3/4 = 19/4
19/4 = 57/12
1/3 = 4/12
57/12 - 4/12 = 53/12 = 4 5/12
One serving of yogurt has 95 calories.
What is the reasonable
estimate for the number of calories in 2.5 servings of
yogurt ?
Answer:
About 300 calories
The drawing will help
our class voted for treasurer.there are 20 students.after voting billy received 3 times more votes then keeton.how many votes did billy receive?
Answer:
Votes received by Billy =15
Step-by-step explanation:
Given:
Total students in the class = 20
Billy receives 3 times more vote than Keeton.
To find the number of votes Billy receives.
Solution:
Let number of votes Keeton gets [tex]=x[/tex]
∴ Billy received [tex]=3x[/tex] votes
Expression for total votes can be given by ⇒ [tex]x+3x[/tex]
Total votes =20 as number of students is 20.
So, the equation to find [tex]x[/tex] is:
[tex]x+3x=20[/tex]
Solving for [tex]x[/tex]
⇒ [tex]4x=20[/tex]
Dividing both sides by 4.
[tex]\frac{4x}{4}=\frac{20}{4}[/tex]
∴ [tex]x=5[/tex]
∴ Votes received by Keeton = 5
Votes received by Billy = [tex]3\times 5[/tex] = 15
The manager at Gabriela's Furniture Store is trying to figure out how much to charge for a book shelf that just arrived. The book shelf was bought at a wholesale price of $147.00 and Gabriela's Furniture Store marks up all furniture by 60 percent.
At what price should the manager sell the book shelf?
The manager should sale the bookshelf for $235.20
Step-by-step explanation:
Wholesale price of book shelf = $147.00
Mark up = 60% of original price
[tex]Mark\ up=\frac{60}{100}*147.00\\\\ Mark\ up=\frac{8820}{100}\\Mark\ up=\$88.20[/tex]
Total = Wholesale price + Mark up
[tex]Total= 147.00+88.20\\Total=\$235.20[/tex]
The manager should sale the bookshelf for $235.20
Keywords: mark up, percentage
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if a= -0.5 and b=5, find the value of 4a+b
When [tex]\(a = -0.5\) and \(b = 5\), the value of \(4a + b\) is \(3\).[/tex]
To find the value of [tex]\(4a + b\) when \(a = -0.5\) and \(b = 5\)[/tex], we simply substitute the values of a and b into the expression 4a+b and then perform the arithmetic.
Given that [tex]\(a = -0.5\) and \(b = 5\)[/tex], we have:
[tex]\[4a + b = 4(-0.5) + 5\][/tex]
Now, let's calculate:
[tex]\[4a + b = -2 + 5\]\[4a + b = 3\][/tex]
Which are solutions of the equation (x+5)(x - 3) = 0? Check all that apply.
x= -15
x=-5
X=-3
x= 2
x=3
x=5
ای
Answer:
x=-5, 3
Step-by-step explanation:
(x+5)(x-3)=0
Apply the zero property,
set x+5=0 and x-3=0.
x=0-5=-5
x=0+3=3
x=-5, 3
Answer:
b&e
Step-by-step explanation:
What is the value of x in the equation? 5 1 10 x − 6 4 5 = 3 1 4 A) 1 1 9 B) 1 1 5 C) 1 3 20 D) 1 33 34
The value of x in the equation is 11/15.
Explanation:To find the value of x in the equation 5 1 10 x - 6 4 5 = 3 1 4, we need to isolate x on one side of the equation. Here's how you can solve it:
Step 1: Add 645 to both sides of the equation.
Step 2: Subtract 314 from both sides of the equation.
Step 3: Simplify the equation.
Step 4: Divide both sides of the equation by 510.
Step 5: Simplify the fraction.
Therefore, the value of x in the equation is 11/15, which is option B) 11/15.
2 FUIILS
A clothing store sells T-shirts, t, for $8 a shirt, and shorts, s, for $12 each. The
store earned $180 revenue last month. The store sold three times as many T-
shirts as shorts. Which system of equations represents this scenario?
8t+12s=180 and t=3s is the system of equations that represents the given scenario.
Step-by-step explanation:
Given,
Cost of a t-shirt = $8
Cost of a shorts = $12
t-shirt = t
shorts = s
Revenue earned = $180
According to given statement;
8t+12s=180
The store sold three times as many T- shirts as shorts.
t = 3s
8t+12s=180 and t=3s is the system of equations that represents the given scenario.
Keywords: linear equation, revenue
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Answer: 8t+12s=180;t=3s APEX
1.since it is a ratio of two integers 2 over 3 is irrational... true or false.
2.since it is a terminating decimal 8.32 is rational..true or false
Answer:
1. false
2. true
Step-by-step explanation:
1. false because fractions are rational
2. true because it can be turned into a fraction
solve the equation for y
[tex] - 3x + 8y = - 48[/tex]
-3x +8y = -48
Add 3x to both sides:
8y = 3x -48
Divide each term by 8:
y = 3x/8 - 6
Answer Y=-45/8
Step-by-step explanation:
-3+8y=-48
-3+8y+3=-48+3
8y=-45
8y/8=-45/8
y=-45/8
A ball is thrown and it follows a parabolic path. At each horizontal distance (x) the following equation models the ball’s height (y).
Y=-0.02x^2+0.8x+3
What will the height of the ball be at a distance of 10 feet?
A. 6
B. 7
C. 8
D. 9
Answer D). 9 ft is correct
Height of the ball at a horizontal distance of 10 feet is 9 ft
Step-by-step explanation:
A ball is thrown and it follows a parabolic path. At each horizontal distance (x) the following equation models the ball’s height (y).
Y(x) = [tex]-0.02x^{2} +0.8x+3[/tex]
Question asked is " What will be height (Y) of the ball when X=10 ft "
Simply putting value of X in given equation
we get,
Y(x) = [tex]-0.02x^{2} +0.8x+3[/tex]
Y(x) = [tex]-0.02(10)^{2} +0.8(10)+3[/tex]
Y(x) = [tex]-0.02(100)} +8+3[/tex]
Y(x) = [tex]-2 +8+3[/tex]
Y(x) = [tex]9[/tex]
Therefore, Height of the ball at a horizontal distance of 10 feet is 9 ft
Answer D. 9 ft is correct
The height of the ball at a distance of 10 feet according to the given equation is 9 feet (option D). This was achieved by substituting the value of 10 into the equation.
Explanation:To find the height of the ball at a distance of 10 feet, you need to substitute the value for the horizontal distance (x) in the given equation. The equation modeling the ball's height is: Y=-0.02x^2+0.8x+3. So, we replace x with 10 in this equation, as follows:
Y=-0.02(10)^2+0.8(10)+3 Y=-0.02(100)+8+3 Y=-2+8+3 Y=9
Therefore, the height of the ball at a distance of 10 feet is 9 feet, so option D is correct.
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The seventh grade class supplied bags of snacks and beverages for the school dance They supplied19 more beverages than bags of snacks The dance was supplied with a total of 371 items.
Answer:
14 bags of snacks.
Step-by-step explanation:
x = the first number
y = the second number
x minus y = 3
x plus y = 13
x - y = 3
x + y = 13
3 x = 8 x + y = 13 8 + y = 13 y = 5 x - y = 3 x +y = 13 2x = 16
The first number = 8
The second number = 5
2x = 16
Difference of the numbers is 3
x = 8
8 – 5 = 3
Sum of the numbers is 13
x + y = 13
8 + 5 = 13
8 + y = 13
y = 5
4 snacks plus beverages = 371 beverages = snacks plus 19
The 8th grade class supplied bags of snacks and beverages for the school dance. They supplied 19 more beverages than bags of snacks. The dance was supplied with a total of 371 items.
x = the number of snacks
y = the number of beverages
snacks plus beverages = 371
beverages = snacks plus 19
x + y = 371
y = x + 19
5 x + y = 371
y = x + 19
Number of snacks = 176
Number of beverages = 195
x + x + 19 = 371
2x = 371
total number of snacks = 371
2x = 352
= 371?
371 = 371
x = 176
19 more beverages than snacks
y = x + 19
= 195
y =
195 = 195
y = 195
6 The seventh and eighth grade bands held a joint concert
The seventh and eighth grade bands held a joint concert. Together there were 188 band members. If the eighth grade band is 3 times as big as the seventh grade band, how big is the eighth grade band?
x = size of the 7th grade band
y = size of 8th grade band
7th grade and 8th grade together = 188 8th grade is 3 x 7th grade
x + y = 188
y = 3x
7 x + 3x = 188 x = 47 y = 3(47) y = 141 x + y = 188 y = 3x 4x = 188
7th grade band = 47 students
8th grade band = 141 students
x + 3x = 188
4x = 188
7th and 8th grade together = 188
= 188?
x = 47
188 = 188
y = 3x
8th grade is 3 times as big as 7th grade
y = 3(47)
141 = 3(47)
141 = 141
y = 141
8 x + y = 81 x = 2y earrings plus necklaces = 81
Amy has 81 pieces of jewelry. She has twice as many earrings as she has necklaces
x = number of earrings
y = number of necklaces
earrings plus necklaces = 81
earrings = 2 x necklaces
x + y = 81
x = 2y
9 2y + y = 81 y = 27 x = 2(27) x = 54 x + y = 81 x = 2y 3y = 81 x = 2y
Number of earrings = 54
Number of necklaces = 27
2y + y = 81
3y = 81
81 pieces of jewelry total
= 81?
y = 27
81 = 81
x = 2y
Twice as many earrings as necklaces
x = 2(27)
2(27) = 54
54 = 54
x = 54
10 9x + 6y = 48 6x + 12y = 72 9 rose plus 6 lily = 48
Julia is making candles. In the morning, she made 9 rose candle plates and 6 lily candle plates. They had a total of 48 candles. In evening, she made 6 rose candle plates and 12 lily candle plates. They had a total of 72 candles. How many candles did each plate have?
x = candles on rose plates
y = candles on lily plates
9 rose plus 6 lily = 48
6 rose plus 12 lilly = 72
9x + 6y = 48
6x + 12y = 72
11 x = 2 6(2) + 12y = 72 12y = 60 y = 5 [9x + 6y = 48] (-2) 6x + 12y = 72
Candles on the rose plates = 2
Candles on the lilly plates = 5
-18x - 12y = -96
6x +12y = 72
9 rose and 6 lilly is 48 plates
9(2) + 6(5) = 48
-12x = -24
= 48
x = 2
6 rose and 12 lilly is 72 plates
6(2) + 12y = 72
6(2) + 12(5) = 72?
y = 72
= 72
12y = 60
y = 5
12 3 adults plus 12 children = 162 3 adults plus 8 children = 122
The cost of admission to a popular music concert was $162 for 12 children and 3 adults. Admission for another group was $122 for 8 children and 3 adults. How much was the admission for each child and adult?
x = the cost of one adult ticket
y = the cost of one child ticket
3 adults plus 12 children = 162
3 adults plus 8 children = 122
3x + 12y = 162
3x + 8y = 122
13 3x + 12y = 162
[3x + 8y = 122] (-1)
The cost of one adult ticket = $14
The cost of one child ticket = $10
3x + 12y = 162
-3x + -8y = -122
12 children and 3 adults spent $162
12 at $10 and 3 at $14 = $162?
4y = 40
$120 + $42 = $162
y = 10
8 children and 3 adults spent $122
3x + 12(10) = 162
8 at $10 and 3 at $14 = $122?
3x = 162
$80 + $42 = $122
3x = 42
x = 14
Answer:
14
Step-by-step explanation:
The height of trapezoid VWXZ is 8 StartRoot 3 EndRoot units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX. Trapezoid V W X Z is shown. A line is drawn from point W to point Y on side Z X, forming a right angle. Angles W V Z and V Z Y are right angles. The length of V W is 10 and the length of W Y is 8 StartRoot 3 EndRoot. Angle YW X is 30 degrees, and angle W X Y is 60 degrees. Once you you know the length of YX, find the length of the lower base, ZX. 14 units 10 + 4 StartRoot 3 EndRoot units 18 units 10 + 8 StartRoot 3 EndRoot units
Answer:
18
Step-by-step explanation:
The lower base will 18units.
What is trapezoid?quadrilatral whose one opposite sides are parallel.
What is tangent of an angle?The tangent of an angle is the ratio between the opposite side of the angle and the adjacent side of the angle.
tanθ=opposite side/adjacent side
So according to asked question
in the trpezoid VWXZ,
VW || XZ
Height of trapezoid= VZ =WY=8√3
VW=10
∠YWX=30°
∠WXY=60°
In triangle ΔWYX,
∠WYX=90°
ΔWYX is a right angle triangle
so, tan∠YWX= XY/WY
⇒tan30°=XY/8√3
⇒1/√3=XY/8√3
⇒XY=8√3/√3
⇒XY=8 units
the length of the lower base ZX= ZY+XY = VW+XY = 10+8=18units
Therefore the lower base will 18units.
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If 8 cases of merchandise cost 60$, what would a dozen cases cost?
Answer: $90
Step-by-step explanation: First, we can change "one dozen" to 12 since it represents the same value.
To find out how much 12 cases of merchandise will cost, we will need to find the unit price per case of merchandise.
Unit price means the cost per unit in this case, the cost per case of merchandise.
Since we know that it costs $60 for 8 cases of merchandise, to find the cost for 1 case of merchandise, we need to divide 8 into $60 or $60 ÷ 8.
60 ÷ 8 = 7.50
Now, we know that it costs $7.50 for 1 case of merchandise.
To find the cost for 12 cases of merchandise, we will multiply the cost for 1 case of merchandise by the number of cases of merchandise we have.
In this case, we will multiply 7.50 by 12 which gives us 90.
Therefore, a dozen cases of merchandise will cost $90.
in the function f(x)=x^2 has the domain of {-2,4,8,9} what is the range
For the function f(x) = x^2 range will be { 4 , 16 , 68 , 81 }
Solution:Given that:
[tex]\text {Function is } f(x)=x^{2}[/tex]
Domain of the function is {-2, 4, 8, 9}
Need to determine range of the function.
Domain of the function is possible input of the function that is x and range of the function is possible output of the function that is f(x)
As there are only four input values for x that are -2,4,8,9 we can determine the range by calculating value of f(x) for each of the x
[tex]\begin{array}{l}{\text {At } x=-2:} \\\\ {f(x)=f(-2)=-2^{2}=4}\end{array}[/tex]
[tex]\begin{array}{l}{\text {At } x=4:} \\\\ {f(x)=f(4)=4^{2}=16}\end{array}[/tex]
[tex]\begin{array}{l}{\text {At } x=8:} \\\\ {f(x)=f(8)=8^{2}=64} \\\\ {\text {At } x=9:} \\\\ {f(x)=f(9)=9^{2}=81}\end{array}[/tex]
Thus the range of given function is { 4 , 16 , 68 , 81 }
Find the differential for P=0.2x^(2)-17x-10
The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17
Step-by-step explanation:
Let us revise how to differentiate an equation with respect to x
If the equation is [tex]y = ax^{n}+b[/tex] , where a , b are constant
The differentiation of the term [tex]ax^{n}[/tex] is [tex]a(n)x^{(n-1)}[/tex] (multiply the coefficient of x by the power"n" and subtract 1 from the power)The differentiation of the term b is 0, because b is a constantThe differentiation of y is [tex]\frac{dy}{dx}=a(n)x^{(n-1)}+0=a(n)x^{(n-1)}[/tex]You can write [tex]\frac{dy}{dx}[/tex] as y'∵ P = 0.2x² - 17x - 10
- Let us differentiate each term
∵ The differentiation of 0.2x² is [tex]0.2(2)x^{2-1}=0.4x^{1}=0.4x[/tex]
∵ The differentiation of -17x is [tex]-17(1)x^{1-1}=-17x^{0}=-17(1)=-17[/tex]
∵ The differentiation of -10 is zero because the differentiation
of the numerical term is 0
∴ The differentiation of P is P' = 0.4x - 17
The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17
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Factor using the distributive property using the GCF
10x-35
Answer:
5(2x-7)
Step-by-step explanation:
what grade is a 259 out of 360 plz help
Answer:
Convert fraction (ratio) 259 / 300 Answer:86.3%
Lisa runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
Answer:
6/55 = x/44
55x = 6(44)
55x = 264
x = 264/55 = 4.8 miles
hope this helps<3
Step-by-step explanation:
Which algebraic expression is equivalent to this expression? 3(2x − 8) – 11x A. -5x – 8 B. -5x – 24 C. -17x – 24 D. -17x – 24
Answer:
B
Step-by-step explanation:
Given
3(2x - 8) - 11x ← distribute parenthesis
= 6x - 24 - 11x ← collect like terms
= - 5x - 24 → B
I’m thinking of three consecutive odd integers. When I add the larger two the result is nine less than three times the smallest of them. What are the three consecutive odd integers?
To find the three consecutive odd integers, we can solve an equation representing the given information.
Explanation:Let the smallest odd integer be x. The next consecutive odd integer will be x + 2, and the largest odd integer will be x + 4.
The problem states that when the larger two integers are added, the result is nine less than three times the smallest integer:
(x + 2) + (x + 4) = 3x - 9
Simplifying the equation, we have:
2x + 6 = 3x - 9
Adding 9 to both sides:
2x + 15 = 3x
Subtracting 2x from both sides:
15 = x
So the smallest odd integer is 15. The consecutive odd integers are 15, 17, and 19.
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What is the equation of the line that has a slope of -4 and goes through (-1,6)?
A. y + 6 = -4(x + 1)
B.
y + 6 = -4(x - 1)
C.
D.
y-6 = -4(x + 1)
y - 6 = -4(x - 1)
Answer:
y-6=-4(x+1)
Step-by-step explanation:
y-y1=m(x-x1)
Where m=slope and (x1, y1) is a point on the line.
m=-4
y-6=-4(x-(-1))
y-6=-4(x+1)
Answer:
y-6=-4(x+1)
Step-by-step explanation:
Plato