Answer:
40
Step-by-step explanation:
[tex]15 \times 2 \frac { 2 } { 3 }\\= 15\times \left(\frac{6+2}{3}\right) \\= 15\times \left(\frac{8}{3}\right) \\= \frac{15\times 8}{3} \\= \frac{120}{3} \\\Longrightarrow \boxed{40}[/tex]
Hope it helps ⚜
look at the simultaneous equations: x+y=a and 2x+y=b. write an expression for x in terms of a and b. write and expression for y in terms of a and b, giving your answer as simply as possible
An expression for x in terms of a and b is y = b - 2x and an expression for y in terms of a and b is y = 2a - b.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A system of equations x + y = a and 2x + y = b.
Now,
x + y = a.
x = a - y and y = a - x.
2x + y = b.
2x = b - y.
x = (b - y)/2.
y = b - 2x.
An expression for x in terms of a and b is,
x + y = a
x + b - 2x = a.
- x = a - b.
x = b - a.
An expression for y in terms of a and b is,
2(a - y) + y = b.
2a - 2y + y = b.
2a - y = b.
- y = b - 2a.
y = 2a - b.
learn more about numerical expressions here :
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Olivia has a dozen apples of the same size
and a dozen pineapples of the same size.
Olivia uses her juicer to extract 12 ounces of
pineapple juice from 7 pineapples and 16
ounces of apple juice from 4 apples. She
makes a pineapple-apple juice blend from an
equal number of pineapples and apples.
What percent of the blend is pineapple juice?
Answer: 30% of the blend is pineapple juice
Step-by-step explanation:
Since 7 pineapples yield 12 oz of juice, 1 pineapple yields 1 5/7 oz of juice.
Since 4 apples yield 16 oz of juice, 1 apple yields 4 oz of juice.
She’s making a pineapple-apple juice where the ratio of apples and pineapples used is 1:1. To find what percent of the blend is pineapple juice:
1 apple to 1 pineapple. The combined amount of juice they produce is 5 5/7 oz. The formula to find what percent of teh blend is pineapple juice is oz of pineapple juice divided by the combined amount of juice in the blend.
1 5/7 divided by 5 5/7 equals 3/10, or 30%.
The fraction of the blend that is pineapple and apple gives the
percentage that is pineapple.
Response:
The percentage of the blend that is pineapple juice is 30%How can the percentage of pineapple juice in the blend be calculated?Amount of juice extracted from 7 pineapples = 12 ounces
Amount of juice extracted from 4 apples = 16 ounces
Therefore;
The amount of juice from 1 pineapple = [tex]\mathbf{\frac{12}{7}}[/tex] ounces = [tex]1\frac{5}{7}[/tex] ounceThe amount of juice from 1 apple = [tex]\frac{16}{4}[/tex] ounces
The amount of juice from 1 apple = 4 ouncesWhich gives;
The amount of juice from 1 pineapple and 1 apple = [tex]\frac{12}{7}[/tex] + 4 = [tex]\frac{40}{7}[/tex] = [tex]5\frac{5}{7}[/tex]
The amount of juice from 1 pineapple and 1 apple = [tex]5\frac{5}{7}[/tex] ouncesThe percentage of pineapple juice is therefore;
[tex]Percentage \ pineapple \ juice \ in \ blend= \dfrac{\dfrac{12}{7} }{\dfrac{40}{7} } \times 100 = \dfrac{12}{7} \times \dfrac{7}{40} \times 100 = \underline{30\% }[/tex]Learn more about percentages here:
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In △ABC,c=9, m∠B=65°, and a=105. Find b.
Answer:
Step-by-step explanation:
b² = a² + c² - 2ac × cos (m∠B)
b² = 105² + 9² - 2(9)(105)cos65°
b ≈ 101.5
Lynn ate lunch and wanted to leave her waitress 15% tip. her meal cost 8.95$. what is the tip and the total
Answer:
Tip would be 1.34
Step-by-step explanation:
total would be 10.29
Consider the equation 7x+2(x+5)=9x+10.
(a) Show that x=-5 and x = 2 are both solutions to this equation.
Answer:
7*-5+2(-5+5)=-35
9*-5+10=-35
7*2+2(2+5)=28
9*2+10=28
Step-by-step explanation:
when plugging the x values in, you get the same answer for both equation, make the equation equal.
Problem 4: Solve the initial value problem
[tex]y' = (y + 1)(y - 2)[/tex]
[tex]y(0) = 1[/tex]
Separate the variables:
[tex]y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx[/tex]
Separate the left side into partial fractions. We want coefficients a and b such that
[tex]\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}[/tex]
[tex]\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}[/tex]
[tex]\implies 1 = a(y-2)+b(y+1)[/tex]
[tex]\implies 1 = (a+b)y - 2a+b[/tex]
[tex]\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13[/tex]
So we have
[tex]\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx[/tex]
Integrating both sides yields
[tex]\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx[/tex]
[tex]\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C[/tex]
[tex]\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C[/tex]
[tex]\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C[/tex]
[tex]\dfrac{y-2}{y+1} = e^{3x + C}[/tex]
[tex]\dfrac{y-2}{y+1} = Ce^{3x}[/tex]
With the initial condition y(0) = 1, we find
[tex]\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12[/tex]
so that the particular solution is
[tex]\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}[/tex]
It's not too hard to solve explicitly for y; notice that
[tex]\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}[/tex]
Then
[tex]1 - \dfrac3{y+1} = -\dfrac12 e^{3x}[/tex]
[tex]\dfrac3{y+1} = 1 + \dfrac12 e^{3x}[/tex]
[tex]\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}[/tex]
[tex]y+1 = \dfrac6{2+e^{3x}}[/tex]
[tex]y = \dfrac6{2+e^{3x}} - 1[/tex]
[tex]\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}[/tex]
Help I Will Give Brainliest If Correct
Hi!
The formula for volume is length * width * height
We are given the area of the base of the figure and the height.
The volume for area is length * width
That means that the length * width part of the volume formula is already done, so we just have to multiply that by the height.
[tex]3 \frac{3}{8}[/tex] * [tex]2[/tex]
[tex]6 \frac{6}{8}[/tex] [tex]= 6\frac{3}{4}[/tex]
For other volume-related questions, see:
https://brainly.com/question/18571772
We know that:
Volume = L × B × HIf L and B are multiplied, they will find the area of the base.L × B = Area of base of rectangular prism.If L and B are multiplied, they will find the area of the base.
This means that:
Area of base of rectangular prism = L × B = 3 3/8 units²Volume = Area of base of rectangular prism × HSubstitute the area of base of rectangular prism in the volume formula.
Volume = Area of base of rectangular prism × H=> Volume = 3 3/8 × HSubstitute the height in the volume formula.
=> Volume = 3 3/8 × 2You can further solve this in two methods. You can use any of them.
Method #1:Convert the mixed fractions into improper fraction.
=> Volume = [(3 × 8 + 3)/8] × 2=> Volume = [(24 + 3)/8] × 2 [Multiplication first]=> Volume = [(27)/8] × 2=> Volume = 27/8 × 2Multiply the fractions
=> Volume = 54/8 units³ = 27/4 units³Convert the volume into mixed fraction:
27/4 = 24/4 + 3/4 = 6 + 3/4 = 6 3/4 units³Method #2:Break 3 3/8 into smaller parts:
(3 3/8) × 2=> (24/8 + 3/8) × 2Simplify the distributive property:
=> 2(3) + 2(3/8)=> 6 + 6/8 = 6 6/8 = 6 3/4 units³Likewise, you can use any method, it will give the same result.
~If you have questions about my answer, don't hesitate to post it in the comments~
Hoped this helped!
1. Physicians There are about 900,000 active physicians in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different sam- ples of 40 physicians are randomly selected, and the mean annual income is computed for each sample.
a. What is the approximate shape of the distribution of the sample means (uniform, normal, skewed, other)?
b. What value do the sample means target? That is, what is the mean of all such sample means?
Using the Central Limit Theorem, it is found that:
a) The shape is approximately normal.
b) It targets the population mean.
Central Limit TheoremThe Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
Item a:
The variable is skewed, however, the sample size is greater than 30, hence the approximate shape of the distribution is normal.
Item b:
According to the mean of the sampling distributions, given by the Central Limit Theorem, it targets the population mean.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Which statement is true?
A The value of x is 116, because the two angles shown add up to 180
B. The value of x is 64 because the two angles shown are congruent
C. The value of x is 26. because the two angles shown are complementary
D. The value of x is less than 90 because the two angles shown are acute angles
Answer:
A
Step-by-step explanation:
Sum of angles in a straight line is 180°
180° - 64° = 116°
Write the recursive formula for the following sequence:
16, 8, 4, 2, ...
Answer:
Answer is in the image
HOPE IT HELPS, BE SAFE KIDDO :3
The sum of 3, 4, and a number amounts to 16
Find the value of x. (For your answer, just type the
NUMBER. Do not put x = .)
Answer:
9
Step-by-step explanation:
The lines are parellel, so you use the formula 7x+12=9x-6 to solve for x.
PLEASE HELP FOR MY MATH PROJECT
A family with 3 adults and 3 children purchase 6 lines each for $35 at ATT. Another family with 2 adults and 4 children purchase 6 lines each for $25 at A-Mobile. Solve for X and Y
what does X and Y represent? I've solved this equation (i got 65 and 5) what do they represent?
Answer:
Step-by-step explanation:
X would be adults Y would be children
3x+3y=35
2x+4y=25
One of the variables have to be equal to each other. So multiply all the terms in the bottom equation by 1.5
You get 3x+6y=37.5
Subtract one equation from another
3x+3y=35
3x+6y=37.5
You get 3y=2.5
Divide both sides by 3
y = 5/6
Now do the same but for X
Multiply the equation by 4/3
4x+4y=46 2/3
Minus the other equation
2x=21 2/3
Divide by 2
x = 10 5/6
Plug numbers in to double check, and they check out
An equivalent fraction to 5/16 is 10/32 correct?
Answer:
correct
Step-by-step explanation:
Yes.
You multiply both 5 and 16 by the same number, 2, to get 10/32.
What is the slope of the line represented by the equation y = -1/2x + ¼?
Given :-
y = -1/2x + 1/4To Find :-
The slope of the equation .Solution :-
Here a equation is given to us and we need to find out the slope of the line . The given equation is ,
→ y = -1/2x + 1/4
We know that slope intercept form of the line is ,
→ y = mx + c
where m is the slope of the line .
On comparing ,
→ m = -1/2
Hence the slope of the line is -1/2.
I hope this helps .
Kenzie bakes 9 oatmeal cookies. Kenzie bakes 7 fewer
cookies than Lisa. How many oatmeal cookies does
Lisa bake?
Answer:
16 oatmeal cookies
Step-by-step explanation:
We can represent this situation as an equation.
L - 7 = 9 L represents Lisa's cookies, (-7) represents 7 fewer cookies, and 9 represents Kenzie's cookiesStep 1: Add 7 to both sides.
[tex]L-7+7=9+7[/tex] [tex]L=16[/tex]Therefore, Lisa baked 16 oatmeal cookies.
Whats point slope formula again
i forgot-
Answer:
● Whats point slope formula
[tex]➢ \: formula = y - {y}^{1} = m \: (x - {x}^{1} \\ y = coordinate \: of \: second \: point \\ {y}^{1} \: coordinate \: of \: point \: one \\ m = slope \\ x = coordinate \: of \: second \: point \\ {x}^{1} = coordinate \: of \: point \: one.[/tex]
[tex]TextFromYourMrEx[/tex]
#CarryOnLearning
Hi!
I can help you with joy! :)
Remember, point-slope form
[tex]\rm{y-y1=m(x-x1)[/tex]
Where
y1 is the y-coordinate of the point
m is the slope
x1 is the x-coordinate of the point
Hope it helps!
Enjoy your day!
[tex]\bf{erutaNtneliS[/tex]
Would be appreciated if someone could help on this transformation question
A. -105
B. -75
C. 75
D. 105
Answer:
B. -75
Step-by-step explanation:
Consider segments AC and A'C'. Point A' is clockwise from point A by an amount less than 90°. Positive angles are measured counterclockwise, so this suggests the angle of rotation is about -75°.
__
In the attached, we have used the invariant point on segments AC and A'C' as the vertex of the angle we want to measure. The angle between the lines appears to be about 75°, matching the answer choices.
Which number does not
belong to the pattern below? Explain.
5,470, 547, 54.7, 0.547
writing to explain tyler has 83 footballs cards that he wants to put into an album. each page holds 6 cards. how many pages will he need? how many spaces will he have left for new cards? explain to awnser.
Since tyler has 83 football cards we can divided, 83 divided by 6 cards for each page would have 13 cards, and he would have an extra page making 14 with the last one containing 5 left over cards, this would leave one space left over for new cards.
Translate the sentence into an equation.
Twice the difference of a number and 7 is equal to 9 .
Use the variable Y for the unknown number.
Answer:
equation: 2(Y-7) = 9
Here the number is twice the difference.the difference is 7, so Y - 7Equals to 9.Six times the sum of a number and 20 is at least 26. Use the variable b for the unknown number.
Answer:
6(b + 20) ≥ 26
Step-by-step explanation:
6(b + 20) ≥ 26
Answer:
6(b + 20) ≥ 26
b ≥ -15 2/3
Step-by-step explanation:
6(b + 20) ≥ 26
6b + 120 ≥ 26
6b ≥ -94
b ≥ -15 2/3
factorise 8x+12 please
Answer: 4(2x+3)
Step-by-step explanation:
The greatest common factor in the two terms is 4.
Therefore, by factoring out a 4 we get
4(2x+3)
Can someone help me with this geometry question!? ASAP
Answer:
D.
I hope it's help:))))))))))))))
A square has 12 cm length and it's area is equal to the area of a rectangle having length 16 cm.What is the breadth of the rectangle?
Step-by-step explanation:
Hope this helps you......
[tex] \displaystyle{ \blue{ \frak{DisneyPrincess29}}}[/tex]
Answer:
Breadth = 9 cm
Explanation:
Find the area of square using; area of square: length²area of the square:
→ 12²
→ 144 cm²
The rectangle has similar area. rectangle area: 144 cm²use the formula to find area of rectangle:
length * breadth = area of rectangleusing the formula:
→ length * breath = 144
→ 16 * breadth = 144
→ breadth = 144/ 6
→ breadth = 9 cm
if 9<15mx-8<27, where m is a positive constant, what is the possible range of values of 8/3 -5mx?
Answer:
Any value greater than -9 and less than -3
Step-by-step explanation:
Explained and uploaded
can someone help me with this question?
Answer:
The answer is D.
Step-by-step explanation:
Which expression is a fourth root of -1 + i sqrt{3} please help
Answer:
r e^iT = r cos T + i r sin T
r cos T = -1
r sin T = sqrt 3
30, 60 90 triangle in second quadrant r = 2, T = 180-60 = 120
so
2e^120i
foruth root is 2^.25 e^(120/4)i
2^.25 e^30 i
2^.25 ( cos 30 + i sin 30)
Step-by-step explanation:
Richard tosses a football with an initial velocity of 10ft/sec from an initial height of 6ft. What is the maximum height the ball will reach?
A. About 7.6ft
B. About 0.3ft
C. 1ft
D. 6ft
Answer: A
The maximum height the ball will reach is 7.6 ft.
Maximum height of the projectileThe maximum height attained by the projectile is calculated as follows;
v² = u² - 2gh
where;
v is the final velocity at maximum height = 0u is the initial velocityh is the heightg is acceleration due to gravity0 = u² - 2gh
2gh = u²
[tex]h = \frac{u^2}{2g} \\\\h = \frac{10^2}{2(32.2)} \\\\h = 1.6 \ ft[/tex]
Thus, the maximum height the ball will reach = 1.6 ft + 6ft = 7.6 ft.
Learn more about maximum height here: https://brainly.com/question/12446886
If a> 1 then prove that a^2>1
Step-by-step explanation:
a² = a × a
a > 1
a² = (1+d) × (1+d) = 1² + 2d + d²
with d > 0
since d > 0, then so is 2d and also d².
so, a² is the sum of 1² = 1 and something greater than 0.
so, a² > 1