Therefore, 110 calories are in 1 serving of milk.
Given, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda.
Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk.
Marian consumes 510 calories by drinking 3 servings of milk and 1 soda.
What are Linear Programming problems?Linear programming, commonly known as LP, is a straightforward technique for representing complex real-world interactions by means of a linear function.
Now,
Let the calories in one serving of milk be x
Let the calories in one serving of juice be y
Let the calories in one serving of soda be z
For Joe, the equation to show the amount of calories is
2x + y + z = 530 -----(1)
For Darius, the equation to show the amount of calories is
x + 2y = 370 ------(2)
For Marian, the equation to show the amount of calories is
3x + z = 510 ------(3)
Now, y=370/2-x/2 and z=510-3x substitute in the equation 2x + y + z = 530.
2x+185-0.5x+510-3x=530
⇒695-1.5x=530
⇒1.5x=165
⇒x=110 calories
Hence, 110 calories are in 1 serving of milk.
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Find the volume (m^3) of the rectangular prism. 5 m 10 m 4 m
Answer:
200m^3.
Step-by-step explanation:
Volume of a rectangular prism = lenght x width x height.
(5m)(10m)(4m) = 200m^3.
Fill in the missing number in this sequence:
400, 200, { } , 50, 25
Answer:
100
Step-by-step explanation:
In this sequence, we can observe that the consistent change between each number in the series is divided by half.
From 400, we divide by 2 to get 200.
400 / 2 = 200
From 50, we divide by 2 to get 25.
50 / 2 = 25
So, to fill in the number after 200, we should logically divide by 2:
200 / 2 = 100
100 also fits into the following numbers, because 100 / 2 is 5.
Answer:
The missing number would be 100
Step-by-step explanation:
You're essentially cutting the numbers in half. For example:
half of 400 would be 200
half of 200 is 100
half of 100 is 50
half of 50 is 25
Without using the formula, work out the gradient of the graph shown.
Answer:
1/3
Step-by-step explanation:
Solve for x. 2^x-1 = 31, give your rounded answer to four decimal places.
The value of x for the given equation is 5.
What is Equation?An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. The most basic and common algebraic equations in math consist of one or more variables.
Here, as per the given Equation
[tex]2^x-1 = 31[/tex]
[tex]2^x = 31 + 1[/tex]
[tex]2^x = 32[/tex]
[tex]2^x = 2^5[/tex]
On comparing both sides, we get
x = 5
Thus, the value of x for the given equation is 5.
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Please just help me with my last 3 question 8 and 9 area and perimeter
♡♡♡ ▲ ▲ ▲ ▲ Ratio of hearts to triangles in simplest form.
3 hearts
4 triangle
H:T
3:4
So, ratio of hearts to triangles in simplest form is 3:4
(we can't simplify any further - HCF of 3 & 4 is 1)
Hope this helps!
What is the probability of rolling two dice, and having a total of 8 dots showing? Express your answer as a percent
rounded to the nearest hundredth.
11.11%
15%
16.67%
13.89%
Show problem set up for full credit.
Answer:
If the arcs are the same
4x+25=5x
x=25
So, QPR is 4(25)+25
QPR is 125
can someone please help me with this
Answer:
[tex]d = \sqrt{109}[/tex]
Step-by-step explanation:
Use the distance formula.
[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Your points are (-4, 11) and (6, 8).
[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]
What is the quotient if 4/15 of 40 is divided by 1/2 of 1/8?
Answer:
l
Step-by-step explanation:
Someone please help fast!
Simplify: in the picture
Answer:
-3ab
Step-by-step explanation:
-27/9= 3
(a^2)/a=a
(b^2)/b=b
(3x-2)(3x-2)(3x-2)(2x+1)
n triangle ABC (see sketch), AD is the angle bisector of the angle A and BH is the height from side AC. The obtuse angle between BH and AD is four times the side of DAB. How big is the angle CAB?
A. 30 B.45 C.60 D.75 E.90
Answer: C
Step-by-step explanation:
We know that [tex]\angle AHB=90^{\circ}[/tex], and thus by the exterior angle theorem,
[tex]90^{\circ}+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^{\circ}[/tex]
Thus, [tex]\angle CAB=2\theta=\boxed{60^{\circ}}[/tex]
The sum of four consecutive integers is -6. What are the four integers?
Answer:
-3 ,-2 ,-1, 0
Step-by-step explanation:
x is the smallest integer then, x+x+1+x+2+x+2=-6
4x+6= -6 4x=-12 x= -3 so the integers are..
400 people were asked if they liked their school lunch.10% said yes. 32 of those that said yes were boys.152 of those that were surveyed were girls. Complete the table to display this data. How many boys said no to liking their school lunch?
Using proportions, considering the total number of students, it is found that 216 boys to linking their school lunch.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 400 - 152 = 248 boys were surveyed. 32 said they liked the school lunch and 248 - 32 = 216 said no liking their school lunch.
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This is a dot plot of the number of text messages sent in a day by a sample of students at a local high school. The sample consisted of 30 students and was selected as representative of the population.
a. What do the six values of 0 on the dot plot represent?
b. Since the sample is representative of the population, describe what you think the dot plot of the entire population will look like.
The six values of 0 shown on the dot plot represent that 6 students out of the 30 sampled did not send any text messages daily.
With the sample being representative of the population, a dot plot for the entire population would have the same proportions as the sample but with a larger number of students.
What does the dot plot show?The number of dots above a number indicates the number of students who send that number of text messages daily.
As there are 6 dots over 0, it means that 6 students do not send any text messages daily.
Seeing as the sample is representative of the entire population, a dot plot for the whole school would have a larger number of dots over each number but the proportions would be the same as the sample.
For instance, the proportion of total students who don't send any messages per day is:
= 6 / 30
= 20%
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14.Evaluate the expression 4x2+3y for x = 5 and y =6.
answer?
Step-by-step explanation:
Given: x=5 and y=6
=>4x2+3y
=> 8+3(6)
=> 8+18
=> 26
Hope it helps
The value of this expression is 58
Algebraic expression is a mathematical sentence that involves all mathematical operations.
In an algebra - a real number is always accompanied by some letter, which can represent a variable or unknown.
— To solve this expression, just: change the letters for the numbers and multiply/add.
⚘ Resolution
[tex]\large \sf 4x2+3y[/tex]
[tex]\large \sf 4 \cdot 5 \cdot 2 +3 \cdot 6[/tex]
[tex]\large \sf 40 +18[/tex]
[tex]\red{\boxed{\boxed{\green{\large \sf \ 58 \ }}}}\\[/tex]
Therefore, the value of this expression will be 58
You have one cubic mile of water. you release it at 1000 gallons per
minute. how long will it take to empty??
It will take 764664.6875 days to empty the water
How to determine the time to empty?The given parameters are:
Volume = 1 cubic mileRate = 1000 gallons per minutesThe time is calculated as:
Time = Volume/Rate
So, we have:
Time = 1 cubic mile ÷ 1000 gallons per minute
Convert gallons to cubic mile
Time = 1 cubic mile ÷ (9.0817e-13 * 1000) cubic mile per minute
Divide
Time = 1.10111715 × 10^9 minute
Convert to days
Time = 764664.6875 days
Hence, it will take 764664.6875 days to empty the water
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What is f(x) + f(x) + f(x)?
✔ 3f(x)
3f(x) =
✔ 3x²
Evaluate 3f(2) =
.
Answer:
12
Step-by-step explanation:
The problem statement tells us the definition of 3f(x). In order to find the value of 3f(2), we substitute 2 for x and do the arithmetic.
__
definition3f(x) = 3x² . . . . given
application3f(2) = 3·2² = 3·4 = 12 . . . . . substitute 2 for x
The value of 3f(2) is 12.
Sofia invested $360 in an account in the year 2005, and the value has been growing
exponentially at a constant rate. the value of the account reached $420 in the year
2009. determine the value of the account, to the nearest dollar, in the year 2015.
well, from 2005 to 2009 is 4 years, so, in 4 years that account went from 360 to 420 at a rate "r", let's find that rate.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$420\\ P=\textit{initial amount}\dotfill &360\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4\\ \end{cases} \\\\\\ 420=360(1 + \frac{r}{100})^{4} \implies \cfrac{420}{360}=(1 + \frac{r}{100})^{4}\implies \cfrac{7}{6}=\left( \cfrac{100+r}{100} \right)^4 \\\\\\ \sqrt[4]{\cfrac{7}{6}}=\cfrac{100+r}{100}\implies 100\sqrt[4]{\cfrac{7}{6}}=100+r[/tex]
[tex]100\sqrt[4]{\cfrac{7}{6}}-100=r\implies 3.92899\approx r \\\\[-0.35em] ~\dotfill\\\\ \underset{2015~~ - ~~2005}{\stackrel{\textit{in the year 2015}}{t=10}}\hspace{5em}A=360\left(1 + \frac{3.92899}{100} \right)^{10}\implies A\approx 529.26[/tex]
A country has two political parties, the Reds and the Blues. The 100-member senate has 44 Reds and 56 Blues. How many ways are there to pick a 10 member committee of senators with the same number of Reds as Blues
There are 4.15E12 ways to select the members of the committee to have the same number of Reds as Blues
How to determine the number of ways?The given parameters are:
Reds = 44
Blues = 56
Committee member = 10
To have the same number of Reds as Blues, the committee must have 5 reds and 5 blues.
So, the number of ways is;
Ways = 44C5 * 56C5
Evaluate the combination expressions:
Ways = 1.086008 E+6 * 3.819816 E+6
Evaluate the product
Ways = 4.15E12
Hence, there are 4.15E12 ways to select the members of the committee
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Find the height in feet of the missile after 5 seconds in the air
The height in feet of the missile after 5 seconds in the air is; 875 ft
How to find the height of a Projectile?
We are given the quadratic function of the height in terms of time, x, in seconds as; h(x) = - 17x² + 260x
where;
h(x) is height after x seconds
x seconds is time of missile in air when thrown.
Thus, after five seconds, we have;
h(5) = - 17(5)² + 260(5)
h(5) = -425 + 1300
h(5) = 875 feet
Complete question is;
A missile is launched from the ground. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.
After 1 second, the missile is 243 feet in the air; after 2 seconds, it is 452 feet in the air.
The height of the can be represented by this function:
h(x) = - 17x² + 260x
Find the height, in feet, of the missile after 5 seconds in the air.
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the table shows the cost of the daycare for Lucy's dog this week her dog went 3 full days of day care and 2 half days of day care write an expression for the total cost of this week day care then evaluate the expression
An expression for the total cost of the daycare for Lucy's dog this week is T = 3F + 2H and the total cost is equal to $114.
How to write an expression for the total cost?In this exercise, you're required to write an expression for the total cost of the daycare for Lucy's dog this week. Thus, we would assign a variable to the cost for full-day and half-day day care as follows:
Let the cost for full-day be F.Let the cost for half-day be H.Let total cost be T.Thus, the total cost of the daycare is given by:
T = 3F + 2H
Evaluating the expression, we have:
T = 3(28) + 2(15)
T = 84 + 30
T = $114.
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Work out the value of 2⁰
Answer:
1
Key:
[tex]a^0=1,\:\quad \:a\ne \:0[/tex]Step-by-step explanation:
[tex]2^0=1[/tex]
Consider 8x-4 = 8^10
Find the difference or type
"impossible"
What is the inverse of function f? A) B) C) D)
Plato
Answer:
(7x-3)/-1
Step-by-step explanation:
swap the x and y and then move the y by itself
x=(3-y)/7
7x=3-y
7x-3=-y
(7x-3)/-1=y
A cylindrical tank has diameter 3.2 m and length
12.7 m.
What is the surface area of the tank, to 1 decimal
place?
Answer:
143.8m^2
Step-by-step explanation:
surface area of a cylinder has the formular
2πr(r+h)
from the question,
radius= diameter/2 = 3.2/2 = 1.6m
height (h) = 12.7m
Area= 2× 3.142×1.6(1.6+12.7)
Area= 10.0544(14.3)
Area= 143.77
Area= 143.8m^2 to 1 decimal places
Answer: 174.3
Step-by-step explanation: diameter of cylindrical tank = 3.2m
so radius is half of 3.2m
length= 12.7m
T.S.A of tank = 2pie r ( r+h)
2 x 3.14 x 3.2/2 ( 3.2/2 + 12.7 )
= 174.29
rounding it off to one decimal the answer would be 174.3
440 meters is 14
of the way around the race track. How far is it around the whole race track?
Answer:
440x4=2200
Step-by-step explanation:
I'm guessing you meant 1/4, which is also known as 0.25, and if you know that 440 meters is equal to 1/4th of the whole race track you just have to multiply 440 by 4.
Find the equation that is parallel to 2x-y=7
Answer:
Below
Step-by-step explanation:
Lines that are parallel have the same slope, so all lines parallel to the one given have the same slope as it does. That slope value is most easily seen by transforming the given equation to slope-intercept form
(y = mx + b).
This line would be y = 2x -7, so the slope of any line parallel to it must have a slope value of 2.
Hi there.
[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]
First of all, we can't find the equation of the line that is parallel to the line we are provided with in this problem, which is [tex]\bf{2x-y=7}[/tex], until we convert this equation into another form.
.
.
This form has a name, and it's called "[tex]\bf{Slope-Intercept\:Form}[/tex].
.
.
So first, what we need to do is subtract 2x from both sides:
.
[tex]\bf{-y=7-2x}[/tex]
.
It's not mandatory, but we can re-arrange the terms "7" and "-2x":
.
[tex]\bf{-y=-2x+7}[/tex]
.
Last step: Divide both sides of the equation by -1:
.
[tex]\bf{y=2x-7}[/tex]
.
"-2x" turned into "2x" because a negative number multiplied or divided by a negative number equals a positive number.
.
"7" turned into "-7" because a positive number multiplied or divided by a negative number equals a negative number.
.
Now, our equation is in "Slope-Intercept Form".
.
Remember that "Slope-Intercept Form" looks like this:
.
[tex]\bf{y=mx+b}[/tex].
.
Now what we need to find is the equation of the line.
.
Let's skim through the provided information to see whether or not there's some information that can help us find the equation.
.
We're also provided with the fact that these lines, or equations, are parallel.
.
What that means is if two lines are parallel, their slopes are the same.
.
The slope of the line whose equation we just found is -2 (it's the number next to "x").
.
I hope that this helped clear your doubts; if any are left, please ask.
.
I wish you a nice rest of your day.
.
[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\sf{n}\bf{g}\:\sf{A}\:\bf{L}\sf{e}\bf{t}\sf{t}\bf{e}\sf{r}.[/tex]
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