You roll a 6-sided die. The probability of getting prime is 50%.
Solution:
Given, that we have rolled a 6 – sided die.
We have to find the P(prime) as percentage.
Now, It means that we have to find the probability of getting a prime number on the face.
On rolling a six sided die, the total possible outcomes are 1, 2, 3, 4, 5, 6
Number of possible outcomes = 6
We have to get a prime number on rolling a die
The prime numbers in possible outcomes are 2, 3, 5
So number of favorable outcomes = 3
[tex]\text {Probability of an event as percentage }=\frac{\text { favourable number of outcomes }}{\text { total number of outcomes }} \times 100[/tex]
[tex]\text {Probability of getting prime number on face of die }=\frac{3}{6} \times 100[/tex]
[tex]\begin{array}{l}{\text { P(prime) }=\frac{1}{2} \times 100} \\\\ {\text { P(prime) }=50 \%}\end{array}[/tex]
Hence, probability of getting prime is 50%.
Factor out the coefficient of the variable
The expression 2b+8 factored is
The factorization of the expression 2b + 8 is 2 ( b + 4 ).
Given data:
The expression is represented as 2b + 8.
To factor out the coefficient of the variable in the expression 2b + 8, determine the greatest common factor (GCF) of the terms.
The GCF of 2b and 8 is 2.
So, divide each term by 2 to factor out the coefficient:
2b + 8 = 2(b) + 2(4)
Now, rewrite the expression factored out:
2b + 8 = 2(b + 4)
Hence, the expression 2b + 8 factored is 2(b + 4).
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Question 9 of 15 (1 point)
4.4 Section Exercise 15
Use the problem-solving flowchart.
The sum of four times a number and ten is equal to the difference of the number and seventeen.
Find the number. Round your answer to the nearest integer, if necessary.
As
The number is
The number is -9
Step-by-step explanation:
Let x be the number then according to given statement
[tex]4x+10 = x-17[/tex]
Subtracting 10 from both sides
[tex]4x+10-10 = x-17-10\\4x = x-27[/tex]
Subtracting x from both sides
[tex]4x-x = x-x-27\\3x = -27[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3} = \frac{-27}{3}\\ x = -9[/tex]
Verification:
[tex]4(-9)+10 = -9-17\\-36+10=-26\\-26=-26[/tex]
The number is -9
Keywords: Linear equation, variables
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at first, kai earned a score of 80 on a quiz. He discovered that 5 points had been taken off by mistake. Kai showed the teacher, and the teacher removed the 5-point deduction.
Answer:
then he would made an 85 bc he wouldve got 5 points added on to his quiz
Doctors have two methods of calculating maximum heart rate. With the first method, maximum heart rate, y, in beats per minute is y = 220 − x, where x is the person's age. Maximum heart rate with the second method is shown in the table.
Age, x 20 30 40 50 60
Heart rate (bpm), y 194 187 180 173 166
Which method gives the greater maximum heart rate for a 90−year-old?
The method gives the greater heart rate.
Answer:
The second method gives the greater heart rate.
Step-by-step explanation:
In the second method, the age and heart rate(bpm) are in a linear relationship.
Therefore, the maximum heart rate for a 90-year-old person in the second method is = 194 - (194 - 187)7 = 145 bpm.
{Since, the maximum heart rate in the second method decreases in an A.P. having value at the age of 20 is 194 and it decreases by 7 bpm per 10 years}
Now, in the first method, the maximum heart rate for 90-year-old person is y = 220 - 90 = 130 bpm.
Therefore, the second method gives a greater heart rate. (Answer)
Answer:
The second method (table) gives the greater heart rate.Step-by-step explanation:
The given expression is
[tex]y=220-x[/tex]
Where [tex]x[/tex] is age.
Now, for [tex]x=90[/tex], we have
[tex]y=220-90=130[/tex]
The equation gives 130 bpm for a 90-year-old patient.
Now, if we observe the given table, we would find a pattern there. The heart rate decreases by 7 while ages decreases by 10, so
For 60 y/o we have 166 bpm.
For 70 y/o we have 159 bpm.
For 80 y/o we have 152 bpm.
For 90 y/o we have 145 bpm.
If we compare, the second method (table) gives the greater heart rate.
7x+12=2(1-x)-x solve
Answer:
x = -1
Step-by-step explanation:
Let's solve your equation step-by-step.
7x + 12 = 2(1 − x) − x
Step 1: Simplify both sides of the equation.
7x + 12 = 2(1 − x) − x
7x + 12 = (2) (1) + (2) (− x) + − x (Distribute)
7x + 12 = 2 + − 2x + − x
7x + 12 = (− 2x + − x) + (2) (Combine Like Terms)
7x + 12 = − 3x + 2
7x + 12 = − 3x + 2
Step 2: Add 3x to both sides.
7x + 12 + 3x = − 3x + 2 + 3x
10x + 12 = 2
Step 3: Subtract 12 from both sides.
10x + 12 − 12 = 2 − 12
10x = − 10
Step 4: Divide both sides by 10.
10x/10 = - 10/10
x = - 1
Hope this helps! Sorry if it is confusing!
Steve and carol live 405 miles apart, they start at the same time and travel toward each other, Steve speed is 6mph greater than carols. If they meet in 2.5 hours, find their speed
Answer:
Speed of Carol is 78 mph and that of Steve is 84 mph.
Step-by-step explanation:
Let the speed of Carol is x mph and that of Steve is (x + 6) mph.
If they move towards each other with that speed, then the resultant speed will be (x + x + 6) = (2x + 6) mph
With this resultant speed, they cover 405 miles in 2.5 hours.
So, [tex]2x + 6 = \frac{405}{2.5} = 162[/tex]
⇒ 2x = 156
⇒ x = 78 mph
So, speed of Carol is 78 mph and that of Steve is (78 + 6) = 84 mph. (Answer)
what is the area of a rectangle with a length of 3ft and a width of 16.1 ft
Suppose y varies as x. If y= -7 when x = -14, find x when y = 10.
Answer:
x = 20
Step-by-step explanation:
-7 (2) = -14 so...
10 (2) = 20
i need help solving this problem. someone help pls :)
20y - 60 = 5x
Answer:
Step-by-step explanation:
20y - 60 = 5x
add 60 to both sides:
20y = 5x + 60
divide through by 20:
y = (1/4)x + 3
slope = 1/4
y-intercept = (0, 3)
Two planes just took off from Salt Lake City, UT. The first plane is traveling 3 times as fast as the second plane. After traveling in the same direction for 7.5 hours, they are 1575 miles apart. What is the average speed of each plane? (Hint: Since they are traveling in the same direction, the distance between them will be the difference of their distances.)
Answer:
The average speed of the first plane is 315 mph and that of the second plane is 105 mph.
Step-by-step explanation:
Let us assume that the first plane has speed x mph and that of the second plane is y mph.
So, as per given condition x = 3y ......... (1)
Now, given that after traveling in the same direction for 7.5 hours, they are 1575 miles apart.
So, we write the equation as
7.5x - 7.5y = 1575
⇒ x - y = 210 ........ (2)
Now, solving equation (1) and (2) we get, 3y - y = 210
⇒ 2y = 210
⇒ y = 105 mph
So, from equation (1) we get, x = 3y = 315 mph.
So, the average speed of the first plane is 315 mph and that of the second plane is 105 mph. (Answer)
use distributive property to write in expanded form 3(6+7)=
Expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]
Solution:Need to use distributive property to write the expanded form of 3(6 + 7)
Let’s understand what is distributive property.
The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.
According to distributive property, for numbers a , b and c
[tex]a(b+c)=a \times b+b \times c[/tex] ----- eqn 1
3(6 + 7) can be rewritten as 3 ( 6 + 4 + 3 ) = 3 ( 10 + 3 )
Now in our case a = 3 , b = 10 and c = 3
On substituting the values of a , b and c in equation 1 we get
[tex]3(10+3)=3 \times 10+3 \times 3=3 \times 10+9 \times 1[/tex]
So expanded form of 3( 6 + 7) is [tex]3 \times 10+9 \times 1[/tex]
PLEASE HELP ME me me me
Answer:
Andre has the correct answer. When simplified his answer is equivalent to the original equation.
Answer:
2pg1
Step-by-step explanation:
Hehe
how do you work out 7/6 divided by 3/11
Answer: 4 and 5/18
Step-by-step explanation: In this problem, we have 7/6 divided by 3/11. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction.
So here, 7/6 ÷ 3/11 can be rewritten as 7/6 × 11/3.
Now we are simply multiplying fractions so we multiply across the numerators and multiply across the denominators.
So we have 7 × 11 which is 77 and 6 × 3 which is 18.
Now we have the fraction 77/18.
We can write 77/18 as a mixed number by dividing the denominator of the fraction into the numerator.
18 divides into 77 4 times with a remainder of 5.
So we can write 77/18 as 4 and 5/18.
Notice that the 18 stays which is the denominator of our original answer.
This means that 7/6 ÷ 3/11 = 4 and 5/18.
Drag steps in the given order to evaluate this expression.
(−3)(2)−7(−3)−10
−37
17
5
−6−21−10
−6−−21−10
−17
Expression
(−3)(2)−7(−3)−10
Perform Multiplication
Simplify
(sort the −37
17
5
−6−21−10
−6−−21−10
−17
into the groups of
Expression
Perform Multiplication
Simplify
Answer:
5
Step-by-step explanation:
(-3)(2)-7(-3)-10
-6+21-10
15-10
5
- y + 8x = -2 for x = 0, 1, 2
Answer:
- y + 8(0) = -2 -y + 8(1)=-2 -y + 8(2) = -2
-y + 0 =-2 -y + 8 - 8 = -2 -8 -y +16 - 16 = -2 -16
-y= -2 -y = -10 -y = -18
Step-by-step explanation:
- y + 8(0) = -2 -y + 8(1)=-2 -y + 8(2) = -2
-y + 0 =-2 -y + 8 - 8 = -2 -8 -y +16 - 16 = -2 -16
-y= -2 -y = -10 -y = -18
for x = 0, 1, 2
The corresponding y values for the given x values (0, 1, 2) into the linear equation y + 8x = -2 is equal to -2, -10, and -18, respectively, it illustrates how the y value changes with different x values in a linear equation.
The linear equation y + 8x = -2 for given values of x (0, 1, 2).
Let's solve it step-by-step for each x value:
For x = 0: Substitute x with 0 in the equation, y + 8(0) = -2, which simplifies to y = -2.
For x = 1: Substitute x with 1 in the equation, y + 8(1) = -2, resulting in y = -10.
For x = 2: Substitute x with 2 in the equation, y + 8(2) = -2, simplifying to y = -18.
This exercise demonstrates how changing the value of x affects the corresponding value of y in a linear equation.
It highlights the importance of substitution in solving equations and understanding linear relationships.
The sum of three times a number and -4 is at least twice the number plus 8 as an inequality
Final answer:
To translate the given statement into an inequality, it converts to 3x - 4 ≥ 2x + 8. Through simplification, we find that x must be at least 12. This showcases the application of basic algebra rules and solving inequalities.
Explanation:
The question asks to translate 'The sum of three times a number and -4 is at least twice the number plus 8' into an inequality. This can be put into mathematical terms as 3x - 4 ≥ 2x + 8, where 'x' represents the unknown number. To solve, we follow several steps:
Subtract 2x from both sides, resulting in x - 4 ≥ 8.
Add 4 to both sides to isolate the variable, giving x ≥ 12.
This inequality tells us that for the original statement to hold true, the number (x) must be 12 or greater. The process involves understanding operations with numbers, such as adding, subtracting, and applying the rules of inequality to solve for 'x'.
If sin (2x+7)= cos(4x-7), what is the value of x
Answer: 15
Step-by-step explanation:
Recall : if sin α = cos β , then α + β are complementary , that is
α + β = 90
Since sin (2x+7) = cos(4x-7) , then (2x+7) and (4x-7) are complementary , that is:
2x + 7 + 4x - 7 = 90
6x = 90
x = 90/6
x = 15
The missing value x is constituting the angles of both sin and cos trigonometric ratios.
By using complementary property, the value of x for given condition is evaluated as 15.
Given that:sin(2x + 7) = cos(4x - 7)Explanation and calculations for value of x:The missing value x is constituting the angles of both sin and cos trigonometric ratios.
Its known by trigonometry that when [tex]sin(\alpha) = cos(\beta)[/tex], then [tex]\alpha + \beta = 90^{\circ}[/tex]
Thus, we have:
[tex]2x + 7 + 4x - 7 = 90\\\\6x = 90\\\\x = \dfrac{90}{6}\\\\x = 15[/tex]
Thus, value of x for given condition is 15.
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How do you solve the equation x over 4 +2 = -12
For this case we must solve the following equation:
[tex]\frac {x} {4} + 2 = -12[/tex]
Subtracting 2 from both sides of the equation we have:
[tex]\frac {x} {4} = - 12-2[/tex]
Equal signs are added and the same sign is placed.
[tex]\frac {x} {4} = - 14[/tex]
Multiplying by 4 on both sides of the equation we have:
[tex]x = -14 * 4\\x = -56[/tex]
Thus, the solution of the equation is [tex]x = -56[/tex]
Answer:
[tex]x = -56[/tex]
Change these times to the 12-hour clock.
a) 1245
b)
1930
Change these times to the 24-hour clock.
d)
midnight
c)
8:15 pm
Answer:
12.45 pm
7.30 pm
00 00
20 15
The temperature of the ice for an ice hockey match is -7°C. For ice-skating, the temperature of the ice is 2 degrees warmer. What is the temperature of ice for ice-skating?
Answer:
Temperature of the ice for ice-skating = -5 °C
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Temperature of the ice for an ice hockey match = - 7 °C
Temperature for ice- skating is 2 degrees warmer.
2. What is the temperature of the ice for ice-skating?
For the correct calculation, we use this formula:
Temperature for ice-skating = Temperature of the ice for a hockey match + 2
Temperature for ice-skating = -7 + 2
Temperature of the ice for ice-skating = -5 °C
We add 2 to the temperature of the ice for a hockey match because the temperature for ice-skating is described as warmer. If it were described as colder, we should subtract.
Answer:
-5c
Step-by-step explanation:
because basically you subtract because it is below normal
May someone please help me with the equation? I would be so very thankful.
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{4(3x^2y^4)^3}{(2x^3y^5)^4}\implies \cfrac{4(3^3x^{2\cdot 3}y^{4\cdot 3})}{(2^4x^{3\cdot 4}y^{5\cdot 4})}\implies \cfrac{4(27)x^6y^{12}}{16x^{12}y^{20}}\implies \cfrac{108x^6y^{12}}{16x^{12}y^{20}} \\\\\\ \cfrac{108}{16x^{12}x^{-6}y^{20}y^{-12}}\implies \cfrac{108}{16x^{12-6}y^{20-12}}\implies \cfrac{27}{4x^6 y^8}[/tex]
A wagon has a mass of 100 grams and an acceleration of 2 m/s2. What is the force on this wagon?
Answer:
0.2 Newtons
Step-by-step explanation:
Newton's Second Law of Motion states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton's Second Law formula:
F = m * a
Where:
F: the magnitude of the net force, in N
m: the mass of the object, in Kilogram
a: the acceleration of the object, in m/s2
Answer:
The force on this wagon is 0.2 Netwons.Step-by-step explanation:
Givens
[tex]m=100 gr[/tex]
[tex]a= 2m/s^{2}[/tex]
First, we need to transform the mass to kilograms, we know that 1 kilogram equals 1000 grams.
[tex]100gr\frac{1kg}{1000gr} =0.1 kg[/tex]
Then, by Newton's Second Law, we have
[tex]F=ma[/tex]
Replacing each variable
[tex]F=0.1kg(2m/s^{2} )\\F=0.2 N[/tex]
Therefore, the force on this wagon is 0.2 Netwons.
What is the equation of the line written in the form y=mx+b that passes through G and has y-intercept of -3 enter the equation of the line in the box.
Answer:
y=-3x-3
Step-by-step explanation:
The equation of the line written in the form y=mx+b that passes through G and has y-intercept of -3 is y=-3x-3
What is the slope intercept form?The slope-intercept form is y = m x + b, where
m is the slope
b is the y-intercept
Given that the line passes through G and has y-intercept of -3
Now Substitute it in the form of the equation
∴ y = mx - 3
From the given graph we can see that the slope is -3.
Then substitute it in the equation
y = -3x - 3
The new equation is y=-3x-3
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solve for n 2/3(1+n) = -1/2n
Answer:
-1/2 = n
Step-by-step explanation:
2/3(1+n) = -1/2n
2/3 + 2/3n = -1/2n
2/3 + 2/3n - 2/3n = -1/2n
2/3 = -1/2n -2/3n
2/3 = -.5n -.66n
2/3 = -1.16n
2/3/-1.16 = n
.66 - 1.16 =n
-0.5=n
- 1/2 = n
An animal shelter spends $4.50 per day to care for each cat and $8.50 per day to care for each dog. Violet noticed that the shelter spent $219.00 caring for cats and dogs on Thursday. Violet found a record showing that there were a total of 30 cats and dogs on Thursday. How many cats were at the shelter on Thursday?
There were 9 cats on the shelter on thursday
Solution:
Let "a" denote number of cats
Let "b" denote number of dogs
Cost per day for each cat = $ 4.50
Cost per day for each dog = $ 8.50
Given that Violet found a record showing that there were a total of 30 cats and dogs on Thursday
Thus, number of cats + number of dogs = 30
a + b = 30 ------ eqn 1
Also given that Violet noticed that the shelter spent $219.00 caring for cats and dogs on Thursday
Number of cats x cost per day for each cat + Number of dogs x cost per day for each dogs = $ 219
[tex]a \times 4.50 + b \times 8.50 = 219[/tex]
4.5a + 8.50b = 219 ----- eqn 2
Multiply first equation by 4.5
4.5a + 4.5b = 135 ---- eqn 3
Subtract eqn 2 from eqn 3
4.5a + 4.5b = 135
(-)4.5a + 8.50b = 219
---------------------------------
-4b = -84
b = 21
Substitute this y value into the first equation
a + b = 30
a + 21 = 30
a = 9
Thus "a" denotes number of cats, so number of cats on thursday = 9
distance=100km, time=75 minutes, speed=?
Step-by-step explanation:
speed= distance/time
time is meant to be in seconds
1mins = 60 secs
75mins =75 x 60 = 4500
distance is meant to be in metres
1metre= 0.001km
100 km = 100 x 1000= 100000
speed =distance/time
speed = 100000/4500
speed=22.22m/s
Answer:
[tex]\large\boxed{80\dfrac{km}{h}}[/tex]
Step-by-step explanation:
[tex]speed=\dfrac{distance}{times}\\\\\text{We have:}\\\\distance=100km,\ time=75min\\\\1h=60min\to1min=\dfrac{1}{60}h\\\\time=\dfrac{75}{60}h=\dfrac{5}{4}h=1.25h\\\\\text{Substitute:}\\\\speed=\dfrac{100km}{1.25h}=80\dfrac{km}{h}[/tex]
If the dimensions of the foundation on the blueprint are 11 inches by 13 inches, what are the actual
dimensions in feet?
richard and two have a combined age of 17. Richard is 2 years older than twice teos age. how old is richard is teo
Answer:
Teo is 5 and Richard is 12
Step-by-step explanation:
r+t=17
2t+2=r
2t+2+t=17
3t+2=17
3t=15
t=5
r+5=17
r=12
Which is the Best Buy?
Whole wheat weighs 16oz and costs $2.24
Pita weighs 20oz and costs $3.60
7-grain weighs 16oz and costs $2.56
Which is the Best Buy?
Answer:whole wheat
Step-by-step explanation:
Its whole wheat because when you divide the cost by the weight whole wheat is the best deal
Simplify :) Thank you! :3
So this is the answer...
Hope this can help :)