Answer:
10x + 15y ≥ 900
Step-by-step explanation:
She burns 10 calories per minute while biking and 15 calories per minute while running. For each exercise, the number of minutes multiplied by the number of calories burned per minute will give the total number of calories burned.
Calories burned while biking (10x) plus (+) calories burned while running (15y) is at least 900 (≥900).
The inequality that models this situation is therefore
10x+15y≥900
The required inequality that models the given situation is 10x + 15y ≥ 900.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
While biking, she burns 10 calories per minute, and 15 calories per minute while running. The total number of calories burned for each exercise is the number of minutes multiplied by the number of calories burned per minute.
Let x be the number of minutes she spends biking and let y be the number of minutes she spends running.
Calories burned while biking (10x) plus (+) calories burned while running (15y) is at least 900 (≥900).
As per the given situation, the required inequality would be as:
⇒ 10x + 15y ≥ 900
Thus, the required inequality that models the given situation is 10x + 15y ≥ 900.
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The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Answer:
the real solutions are the ones that actually cross the x-axis.
so the real solutions are (-5, 0) (-1,0) (4,0) and (8,0)
A rectangular area of land is being sold off in smaller pieces. The total area of the land is 2^15 square miles. The pieces being sold are 8^3 square miles in size. How many smaller pieces of land can be sold at the stated size? Compute the actual number of pieces.
HELLPP PLS !!!
The number of smaller pieces of land that can be sold at the stated size is 2^6
How many smaller pieces of land can be sold at the stated size?The given parameters are:
Total area = 2^15 square miles
Smaller piece = 8^3 square miles
The number of smaller pieces of land that can be sold at the stated size is
Number = Total area/Smaller piece
So, we have:
Number = 2^15/8^3
Rewrite as
Number = 2^15/2^9
Apply the law of indices
Number = 2^6
Hence, the number of smaller pieces of land that can be sold at the stated size is 2^6
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What is the value of 9 by the power of 2+ 3 by the power of 3 - 30 divided by 6?
HELP MEH PLS!!! I will give Brainlyest to whoever answers first and correctly. Also tell me if I’m wrong dose this ^ symbol mean division?!?!
I do not know how to do this but i can tell you ^ means exponent not division. So 3^2 would be the same as [tex]3^{2}[/tex]
The variables y and x have a proportional relationship, and y = 7 when x = 2 What is the value of x when y = 212 Enter your answer in the box x = 1
Answer:
proportional relational ship
y= kx
7 = k2
solve for k
7/2 =k
y = 7/2 x
if y = 21
21 =7/2 x
solve for x
multiply by 2/7 on each side
21* 2/7 = 2/7*7/2 x
6 =x
Figure out the probability below (ONLY REAL ANSWERS PLEASE)
Answer:
2/35
Step-by-step explanation:
fifteen total, 4 live in Gaston
so
4/15 times 3/14
because there is only 14 left to be selected and 3 left in Gaston
so 0.05714285714
or 2/35
Help please due soon
Answer:
1. H=6
2. Y= -1
3. T= 2
4. D= 2.1
5. K= 0
6. -13 1/3
Step-by-step explanation:
What system of equations is shown on the graph below?
On a coordinate plane, 2 lines intersect around (1.8, negative 0.8).
2 x + y = 3 and 3 x minus 4 y = 8
2 x minus y = 3 and 3 x + 4 y = 8
2 x + y = 3 and 3 x minus 4 y = 2
2 x minus y = 3 and 3 x minus 4 y = negative 2
Answer:
i thnk it is c correct me if i am rong
Step-by-step explanation:
Answer:
(C) I got it right
Step-by-step explanation:
on edge
I need help thank you
Answer:
[tex]4x^2-x+8[/tex]
Step-by-step explanation:
First expand [tex](x-8)^2[/tex].
[tex](x-8)(x-8)=x^2-16x+64[/tex]
Now Add:
[tex](x^2-16x+64)+(3x^2+15x-56)\\(x^2+3x^2)+(-16x+15x)+(64-56)=\\4x^2-x+8[/tex]
We want this:
3x^2 + 15x - 56 + (x - 8)^2
First, expand (x - 8)^2 using FOIL.
So, (x - 8)^2 = (x - 8)(x - 8).
(x - 8)(x - 8) = x^2 - 16x + 64.
We now add like terms.
3x^2 + 15x - 56 + x^2 - 16x + 64
4x^2 - x + 8
Done.
Mark had an essay due on Friday. He worked on the essay for 1.5 hours on Thursday and 4.25 hours on Fridays. How many hours did he work on the essay Thursday and Friday combined?
Answer:
He worked for 5.75 hours
Step-by-step explanation:
Please help I give 20 points please no fake answers =/
Answer:
1 4/5
Step-by-step explanation:
It is 2.1 km from Jessica's house to the nearest mailbox. How far is it in meters?
Be sure to include the correct unit in your answer.
Answer:
2100 meters
Step-by-step explanation:
REMEMBER: 1 km = 1000 m
2.1 km x 1000= 2100 meters
hope this helps ;)
Divide 2x^4+5x^3+11x^2+8x by x^2+x
Use slopes to determine if the lines -7x + 3y = 2 and -3x + 7y = 1 are perpendicular
The slopes of the given lines -7x + 3y = 2 and -3x + 7y = 1 are not perpendicular to each other .
The slope of a line is the ratio of how much y increases when x increases by a certain amount. Slope indicates the slope of the line, i.e. how much y increases as x increases. The slope is constant (the same) everywhere along the straight line. The slope intercept of the straight line is used to find the equation of the straight line. The slope intercept formula requires knowing the slope of the line and the intersection of the line with the y-axis. Consider a straight line with slope 'm' and y-intercept 'c'. The slope-intercept shape formula for a straight line with slopes 'm' and 'c' as y-intercept is given as y = mx + c.
We have given two equation of lines -7x + 3y = 2 ....(1) and -3x + 7y = 1 ....(2) 3y = 7x +2
y = 7x/3 +2
On comparing with slope intercept form y = mx + c , we get slope of equation (1) m₁ = 7/3
7y = 3x +1
y = 3x /7 +1
On comparing with slope intercept form y = mx + c , we get slope of equation (2) m₂ = 3/7
If the lines are perpendicular to each other , then their product of slope will be equal to -1 which is given by
m₁ × m₂ = -1
7/3 × 3/7 = -1
1 ≠ -1
Hence the given lines are not perpendicular to each other.
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How far would the plane fly in t hours at this speed
Answer: 610 MPH
Step-by-step explanation:
915 divided by 1.5=610 MPH
610 divided by 2=305 MP Half n Hour
610+305=915
1500 as a mixed number, please help QUICK
Answer:
divid 1500 to 50
Step-by-step explanation:
Answer: 1500 0/0
Step-by-step explanation:
Choose a system of equations with the same solution as the following system:
4x − y = −11
2x + 3y = 5
A. 12x − 3y = −33
10x − 6y = −38
B. −4x − 9y = −21
−2x − 7y = −27
C. 4x + 3y = 5
10x + 5y = −1
D. 2x − 4y = −16
4x − 4y = 44
please help 100points!!!!
And i will make brainlest
only if the answer is right and there is a good explanation....
Answer:
Hope it can help you and Mark me as a brainlist....
Every month, Theresa sets aside $410.60 of her paycheck to use as spending money. This month, she plans to use 2/5 of her spending money for groceries. How much money would Theresa have this month to spend on items other than groceries?
Answer:
246.36
Step-by-step explanation:
What is the value of f(x)=5-1/2 when x =4
Answer:
9/2
Step-by-step explanation:
f(x)=5-1/2
plug in 4
f=9/2
9/2
Which digit is in the thousandth place? 134.927
Answer:
.007 is in the thousandths place.
Step-by-step explanation:
In decimals it goes tenths, houndredths, thousandths, and so on.
pleasee helppp insert two arithnetic means between -5 and 1
Answer:
a₂ = -3
a₃ = -1
Step-by-step explanation:
We have to insert two arithmetic means between -5 and 1
Let a₁ and b₂ be the two arithmetic means between -5 and 1
-5, a₂, a₃, 1
Here,
a₄ = 1a₁ = -5We know that the nth term of an Arithmetic sequence
aₙ = a₁ + (n-1)d
a₄ = -5 + (4-1)d
1 = -5 + 3d
1 + 5 = 3d
3d = 6
Dividing both sides by 2
d = 2
Also
a₂ = a₁ + (2-1)d
a₂ = -5 + d
a₂ = -5 + 2 ∵ d = 2
a₂ = -3
a₃ = a₁ + (3-1)d
a₃ = -5 + 2d
a₃ = -5 + 2(2) ∵ d = 2
a₃ = -5 + 4
a₃ = -1
Thus,
a₂ = -3
a₃ = -1
Thus, the sequence becomes:
-5, -3, -3, 1
A jar contains only one blue tile, one green tile, one red tile, and one yellow tile. If a tile is chosen at random and then replaced in the jar, and then a second tile is chosen at random, how many of the possible outcomes contain at least one red tile? 1 2 4 7
Answer:
7
Step-by-step explanation:
Bluegreen
Bluered
Blueyellow
Greenblue
Greenred
Greenyellow
Redblue
Redgreen
Redyellow
Yellowblue
Yellowgreen
Yellowred
Answer: 7
Step-by-step explanation:
Took on computer
a) Let X be a random variable that can assume only positive integer values, and assume its probability function is P(X -n) A/3^n for some constant A (n> 1). Find A.
b) Let X be a continuous random variable that can assume values between 0 and 3, and assume its density function is fx(x)- B(x2 +1) with some constant B (0< x ,3). Find B.
Answer:
a) The value of A = 2
b) The value of [tex]B = \dfrac{1}{12}[/tex]
Step-by-step explanation:
a)
Given that:
X should be the random variable that assumes only positive integer values.
The probability function; [tex]P[X = n] = \dfrac{A}{3^n}[/tex] for some constant A and n ≥ 1.
Then, let [tex]\sum \limits ^{\infty}_{n =1} P[X =n] = 1[/tex]
This implies that:
[tex]A \sum \limits ^{\infty}_{n =1} \dfrac{1}{3^n}= 1[/tex]
[tex]A \times \dfrac{\dfrac{1}{3}}{1 - \dfrac{1}{3}} = 1[/tex]
[tex]A \times \dfrac{\dfrac{1}{3}}{\dfrac{2}{3}} = 1[/tex]
[tex]A \times \dfrac{1}{2}=1[/tex]
A = 2
Thus, the value of A = 2
b)
Suppose X represents a e constant A (n> 1). Find A.
b) Let X be a continuous random variable that can assume values between 0 and 3
Then, the density function of x is:
[tex]f_x(x) = \left \{ {{B(x^2+1)} \ \ \ 0 \le x \le 3 \ \ \ \atop {0} \ \ \ otherwise} \right.[/tex]
where; B is constant.
Then, using the property of the probability density function:
[tex]\int ^3_0 \ B (x^2+1 ) \ dx = 1\\[/tex]
Taking the integral, we have:
[tex]B \Big [\dfrac{x^3}{3} +x \Big ]^3_0 = 1[/tex]
[tex]B \Big [\dfrac{3^3}{3} +3 \Big ]= 1[/tex]
[tex]B \Big [\dfrac{27}{3} +3 \Big ] = 1[/tex]
B [ 9 +3 ] = 1
B [ 12 ] = 1
Divide both sides by 12
[tex]B = \dfrac{1}{12}[/tex]
Give two different names for the line shown in the
diagram below.
Answer: segments and rays
Step-by-step explanation:
The Blacktop Speedway is a supplier of automotive parts. Included in stock are 5 speedometers that are correctly calibrated and two that are not. Three speedometers are randomly selected without replacement. Let the random variable
x
represent the number that are not correctly calibrated.
Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.)
x=0,1,2,3
p(x)=
Find the mean of this probability distribution. (Appropriate rounding rules apply.)
mean =
The Probability distribution table is;
x P(x)
0 0.4167
1 0.5
2 0.0833
3 0
How to create probability distribution table?The speedometers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
P(X = x) = h(x, N, n, k) = C_k,x * C_n - k, n - x)/(C_N,n)
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
7 + 2 = 9 speedometers, which means that N = 9
2 are not correctly calibrated, which means that k = 2
3 are chosen, which means that n =3
Complete the probability distribution table.
Probability of each outcome.
P(X = 0) = h(0, 9, 3, 2) = 0.4167
P(X = 1) = h(1, 9, 3, 2) = 0.5
P(X = 2) = h(0, 9, 3, 2) = 0.0833
P(X = 3) = h(0, 9, 3, 2) = 0
Probability distribution table:
x P(x)
0 0.4167
1 0.5
2 0.0833
3 0
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What are fractions? Plz help
Which of the following is NOT a transformation?
Translation
Reflection
Rotation
Construction
Dilation
select the correct answer
Answer:
a) We get [tex]\mathbf{A+B=x^2-2x+1}[/tex]
So, Is the result of A+B is a polynomial:Yes
b) We get [tex]\mathbf{A-B=6x^3-7x^2+2x-1}[/tex]
So, Is the result of A-B is a polynomial:Yes
c) We get [tex]\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}[/tex]
So, Is the result of A.B is a polynomial:Yes
Step-by-step explanation:
We are giving the polynomial equations:
[tex]A= 3x^2(x-1)\\B=-3x^3+4x^2-2x+1[/tex]
We need to find
a) A+B
[tex]A+B=3x^2(x-1)+(-3x^3+4x^2-2x+1)\\A+B=3x^3-3x^2-3x^3+4x^2-2x+1\\A+B=3x^3-3x^3-3x^2+4x^2-2x+1\\A+B=x^2-2x+1\\[/tex]
So, we get [tex]\mathbf{A+B=x^2-2x+1}[/tex]
So, Is the result of A+B is a polynomial:Yes
b) A-B
[tex]A-B=3x^2(x-1)-(-3x^3+4x^2-2x+1)\\A-B=3x^3-3x^2+3x^3-4x^2+2x-1\\A-B=3x^3+3x^3-3x^2-4x^2+2x-1\\A-B=6x^3-7x^2+2x-1\\[/tex]
So, we get [tex]\mathbf{A-B=6x^3-7x^2+2x-1}[/tex]
So, Is the result of A-B is a polynomial:Yes
c) A . B
[tex]A.B=3x^3(-3x^3+4x^2-2x+1)-3x^2(-3x^3+4x^2-2x+1)\\A.B=9x^6+12x^5-6x^4+3x^3+9x^5-12x^4+6x^3-3x^2\\A.B=9x^6+12x^5+9x^5-6x^4-12x^4+3x^3+6x^3-3x^2\\A.B=9x^6+21x^5-18x^4+9x^3-3x^2[/tex]
So, we get [tex]\mathbf{A.B=9x^6+21x^5-18x^4+9x^3-3x^2}[/tex]
So, Is the result of A.B is a polynomial:Yes
John spent $75 on a shopping trip for new clothes last week. He had expected to spend $100 on clothes. A 6-column table with 1 row. Column 1 is labeled Approximate Value with entry 100 dollars. Column 2 is labeled Exact Value with entry 75 dollars. Column 3 is labeled Error with entry 25 dollars. Column 4 is labeled Absolute Error with entry blank. Column 5 is labeled Ratio with entry blank. Column 6 is labeled Percent Error with entry blank. How much was the absolute error in his estimate? $ John spent $75 on a shopping trip for new clothes last week. He had expected to spend $100 on clothes. A 6-column table with 1 row. Column 1 is labeled Approximate Value with entry 100 dollars. Column 2 is labeled Exact Value with entry 75 dollars. Column 3 is labeled Error with entry 25 dollars. Column 4 is labeled Absolute Error with entry blank. Column 5 is labeled Ratio with entry blank. Column 6 is labeled Percent Error with entry blank. How much was the absolute error in his estimate? $
Answer:200
Step-by-step explanation:
All you have to do is add.
Answer:
25
Step-by-step explanation:
because its simple math
anyways have an nice day
To offer scholarships to children of employees, a company invests $10,000 at the end of every 3 months in an annuity that pays 8% compounded quarterly.
a) how much will the company have in scholarship funds at the end of ten years?
b) find the interest
The amount the company will have in scholarship funds at the end of ten years is $604,019.83.
The interest is $204,019.83.
How do we calculate scholarship funds amount and interest?a) The amount the company will have in scholarship funds at the end of ten years can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = P * (((1 + r)^n - 1) / r) ................................. (1)
Where,
FV = Future value or the scholardhip amount after 10 years =?
P = Quarterly payment or payment at the end of every 3 months = $10,000
r = Quaterly interest rate = 8% / 4 = 2%, 0.02
n = number of periods = number of quaters in a year * 10 = 4 * 10 = 40
Substituting the values into equation (1), we have:
FV = $10,000 * (((1 + 0.02)^40 - 1) / 0.02)
FV = $604,019.83
b) The interest can be found as follows:
Total payment = P * n = $10,000 * 40 = $400,000
Interest = FV - Total payment = $604,019.83 - $400,000 = $204,019.83
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Manuel saved $375 in 6 months. At this rate, how much will he save in 2 years?