A ratio shows us the number of times a number contains another number. The maximum amount of purple that Susan can make is 25 ml.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Susan makes purple paint by mixing red and blue paint in a ratio of 2:3. Now, if Susan wants to use the complete red paint then,
Purple paint she can make = 2/3 × 6/6 = 12 ml of red paint / 18 ml of blue paint
If Susan wants to use the complete blue paint then,
Purple paint she can make = 2/3 × 5/5 = 10 ml of red paint / 15 ml of blue paint
As per the first condition 18ml of blue paint is needed which is not possible, therefore, the second case is possible.
Thus, Susan needs to mix 10 ml of red paint and 15 ml of blue paint. Therefore, the amount of paint that Susan will make is,
Total Paint = 10ml + 15ml = 25ml
Hence, the maximum amount of purple that Susan can make is 25 ml.
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Lyanna opens a bank account with a deposit of $200. She earns 3%
interest per year. How much money will Lyanna have in her account after
the first year?
Answer:
$206
Step-by-step explanation:
Lyanna will earn 3% on her capital within 1 year.
In total, she will have 103%.
$200 x 103% = $206
which inequality is equivalent to the given equality of -4(x+7)<3(x-2)
Answer:
x > 22/7
_________________________________________
Notice*
Because there are no options, we must find it algebraically.
_____________________________________________
Let's solve your inequality step-by-step.
−4(x+7)<3(x−2)
Step 1: Simplify both sides of the inequality.
−4x−28<3x−6
Step 2: Subtract 3x from both sides.
−4x−28−3x<3x−6−3x
−7x−28<−6
Step 3: Add 28 to both sides.
−7x−28+28<−6+28
−7x<22
Step 4: Divide both sides by -7.
-7x/-7 = 22/-7
x > -22/7
Answer:
x > −22/7
Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
The function g(x) = ∛(x -3) is positive at the interval x > 3
Complete questionGiven g(x) = ∛(x -3), on what interval is the function positive?
How to determine the positive interval?The function is given as:
g(x) = ∛(x -3)
Set the radicand to positive
x - 3 > 0
Add 3 to both sides
x > 3
Hence, the function is positive at the interval x > 3
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vincent mows 8 lawns in 2 hours. how many lawns are mowed in 5 hours .
Answer:
20 lawns
Step-by-step explanation:
Hii! I need some help, would anyone mind helping me?
Find the center of this hyperbola.
[tex]\boldsymbol{x^2-25y^2-14x+100y-76=0}[/tex]
[tex]\stackrel\bigstar{\boldsymbol{\underbrace{Thankyou!!}}}[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]
Factor by grouping,
[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]
Complete the square, with the x variables,
[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]
Factor out 25 for the y variables
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]
Complete the square
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]
Simplify the perfect square trinomial
[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]
Make the right side be 1 so divide everything by 25.
[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]
Here our center is (7,2).
Hi 6 questions ! They are practice so shouldn’t be to hard!
Please fine the slope through the given points
Answer:
1. 1
2. 6/5
5. 0
6. -1/2
9. -1
10. 0
Step-by-step explanation:
Well you should just the slope formula (y2-y1)/(x2-x1)
1. (8-5)/(0-(-3)) = 3/3 = 1
2. (-3-(-9))/(4-(-1)) = 6/5
5. (3 - 3) / (0-2.5) = 0/(-2.5) = 0
6. (0-(-4))/(0-8) = 4/(-8) = -1/2
9. (4-1)/(9-12) = 3/(-3) = -1
10. (7-7) / (1-(-5)) = 0/6 = 0
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. persons taking a 70-hour review course average a score of 780. based on these two data points, create a linear equation for the function that describes how score varies as a function of time. use this function to predict an average score for persons taking a 43-hour review course. round your answer to the tenths place.
Answer:
Answer for linear equation: y=4x+500 and Avg score for persons taking 43-hour review course is 672
Jamar is attempting to factor the expression 15x^2-16x-15. In his first step, he rewrites the expression as 15x^2-25x+9x-15. Which of the following statements in true about Jamar’s work?
A. Jamar's first step is correct. He should continue to factor the expression.
B. The two middle coefficients add to the correct number, but do not multiply to the correct number.
C. The two middle coefficients multiply to the correct number, but do not add to the correct number.
D. The two middle coefficients do not add or multiply to the correct number.
Jamar's first step is correct. He should continue to factor the expression. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
Jamar is attempting to factor the expression 15x² – 16x – 15.
In his first step, he rewrites the expression as 15x² – 25x + 9x – 15.
Jamar's first step is correct. He should continue to factor the expression.
Then the correct option is A.
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what is the simiplyfly for this -8(-3)
Answer:
24
Step-by-step explanation:
when you open up the parenthesis, you get -8x-3 which is 24.
negative x negative = positive
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years. Which of the following is an appropriate line of best fit?
The equation of the appropriate line of best fit is y = 1.25x + 2
How to determine the line of best fit?Start by drawing a line through the points (see attachment)
From the attached graph, we have:
(x, y) = (0,2) and (4,6.5)
Calculate the slope (m) using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (6.5 - 4)/(2 - 0)
Evaluate
m = 1.25
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1.25(x - 0) + 2
Expand
y = 1.25x + 2
Hence, the equation of the appropriate line of best fit is y = 1.25x + 2
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Dr. Smith and Dr. Jones want to study the effects on a patient's arthritis that curl in the patient believes that he was she use a new ointment the control group consists of the patient who chooses to visit Dr. Smith about arthritis and they receiving an appointment with no medical value the experimental group consists of the patients who chooses to visit Dr. Jones about the right s and they receive the new ointments is this study experimental or observational
Answer:I think observational
Step-by-step explanation:They want to study it so they trying it on people who are willing so they are looking closely to what happens.
Please help me
Find the values of x and y
(12x +15)°=75° .…(शिर्षभिमुख कोण भएर)
or, 12x+15=75
or, 12x=75-15
or, 12x=60
or, x=60÷12
or, x=5
(6y-27)°=105° .…(शिर्षभिमुख कोण भएर)
or, 6y-27=105
or, 6y=105+27
or, 6y=132
or, y=132÷6
or, y=22
I am having some problem can anyone please help me out to do this math.
(x + 3)(x + 4)
Answer:
x^2 + 7x + 12
Step-by-step explanation:
This is a product of two binomials. There's a formula:
(a + b)(c + d) = ac + ad + bc + bd.
Therefore, (x + 3)(x + 4) = x^2 + 3x + 4x + 12 = x^2 + 7x + 12
x(3y - 2)
Multiply this problem
Answer:
3xy-2x
Step-by-step explanation:
Distribute x to both 3y and -2: 3y*x-2*x.
Can you solve these questions and explain them for me? Thank you
Step-by-step explanation:
When folding up the box, x will be the height
(30-2x) will be the length
(25-2x) will be the width so
[tex]v(x) = x(30 - 2x)(25 - 2x)[/tex]
b. First, we can't have negative length or zero length so x must be Positve.
Set the other binomial equal to 0.
[tex]30 - 2x > 0[/tex]
[tex] - 2x > - 30[/tex]
[tex]x < 15[/tex]
[tex]25 - 2x > 0[/tex]
[tex] - 2x > - 25[/tex]
[tex]x < 12.5[/tex]
So our domain is
(0,12.5), meaning our value of x must be greater than 0 and less than 12.5
Which statement about the polynomial function g(x) is true?
1If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
2If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
3If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
4If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.
When leading coefficient is 1 , the root will be an integer for g(x) = 0
Option 4 is the right answer.
What is a Polynomial Function ?Functions of independent variable in which the variable can appear more than once with different powers.
[tex]\rm g(x) = a_n x^n + a_{n-1}x^{n-1} + ................+ a_o[/tex]
Let this represents the polynomial function
where [tex]\rm a_n \; is\;the \;leading \; coefficient \; a_o \; is \;the\;last \;term[/tex]
Then the according to rational root theorem ,
The root of the function is given by
[tex]\rm \dfrac{p}{q} = \dfrac{factor \;of\; the\; last\; term}{factor \;of \;the\; leading coefficient}[/tex]
So when leading coefficient is 1 , the root will be an integer for g(x) = 0
Option 4 is the right answer.
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Given the quadrilateral below is a rhombus, solve for the length of the side of the rhombus.
Answer:
7.21
Step-by-step explanation:
There is a formula to find the area of a side of a rhombus given 2 diagonals.
It is: [tex]\frac{\sqrt{p^{2}+q^{2} } }{2}[/tex]
64 + 144 = 208
[tex]\sqrt{208}[/tex] = 14.42
14.42 / 2 =
7.21
The lottery in our state consists of two drawings. first, a megaball is picked from among 27 numbered balls. second, five winnerballs are picked from among 44 numbered balls. to win the lottery, you must pick the megaball number correctly and also pick the numbers on the five winnerballs (but you don't need to get the order right for the winnerballs). what is the probability that the ticket i hold has the winning numbers
Using the combination formula, it is found that the probability that the ticket i hold has the winning numbers is:
[tex]p = \frac{1}{29,322,216}[/tex].
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For the winnerballs, 5 balls are taken from a set of 44, hence:
[tex]C_{44,5} = \frac{44!}{5!39!} = 1086008[/tex]
Considering the numbered balls, the number of outcomes is given by:
N = 27 x 1086008 = 29,322,216.
Hence the probability is given by:
[tex]p = \frac{1}{29,322,216}[/tex].
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The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)
Answer:
the graph of f(x)= -2-10x+16
Answer:
the vertex would be (-5,41)
Step-by-step explanation:
You just plug the -5 back into the equation to get 41
Please help! Which of the following would result in an integer?
Answer:
B
Step-by-step explanation:
Cube root of 27 is 3, which is in integer
A package of 12 hex bolts and 10 anchor bolts weighs 7 pounds. A second package of 5
hex bolts and 15 anchor bolts weighs 4 pounds. A single hex bolt weighs ___________
pounds, rounded to one decimal place
Answer:
0.5
Step-by-step explanation:
Let h = weight of 1 hex bolt Let a = weight of an one anchor bolt1) (12h + 10a = 7) × 3 ⇒ (1) 36h + 30a = 21
2) (5h + 15 = 4) × -2 ⇒ + (2) - 10h - 30a = 8
----------------------
26h = 13
----- -----
26 26
h = 13 ÷ 13
---
26 ÷ 13
h = 1
---- = 0.5
2
Answer:
1 hex bolt weight 0.5 lbs.
Find the distance-
Which shows the values inputted into the distance formula?
*See photo*
Answer:
A.
Step-by-step explanation:
As shown in the question we can interpret the following:
[tex]x_{1} = -2\\y_{1} = 1\\x_{2} = 5\\y_{2} = -4[/tex]
Now all we have to do is plug these values into the equation, and so we find that A. is the correct answer.
The diameter of a circle is 62cm
by first calculating the radius work out the area of the circle
give your answer in cm² to 1.d.p
Find the number of turns or bumps in the graph of the function f(x) = x² - 25
Answer:
1 turn
Step-by-step explanation:
this is what the graph would look like:
I’m having trouble understanding how to solve this someone please help ASAP thank you!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Answer:
Answer is 71.95°
Step-by-step explanation:
Cosine formula is
a^2=b^2+c^2-2bc(cosA)
cos A =b^2+c^2-a^2/2bc
if a= 119,b=94,c=173
cos A=94^2+173^2-119^2/2(94*173)
=8836+29,929-14,161/2(16,262)
=38765-14,161/32,524
=24604/32,524
=0.7564
cos A=0.7564
cos^-1=40.85°.that's for angle A.
Using the same formula
B=31.1°
C=180-(40.85+31.1)
C=180-71.95
C=108.05
Since angle on a straight line is 180
therefore x is 71.95
Also the sum of angles A and B
Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals. Determine the number of players the team can bring to the tournament. Please step by step
Answer:
20 Players
Step-by-step explanation:
Total Amount of Money: $2412.50
First the team rented us a bus for $1072.50
Subtract the bus from the total
$2412.50 - $1072.50 = $1340
Total Amount of Money after bus: $1340
From there we need to find the max number of players that can go.
The budget cost for each player is $67.
So we divide the remaining money by $67 to find the number of players that can go.
$1340/$67 = 20 Players.
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Hope this helps!
Students are selling T-shirts for a school fundraiser. The table shows the amount they raise from the T-shirt sales.
Shirts Sold 1 2 3 4
Amount Raised (dollars) 4 8 12 16
Complete each statement.
The amount raised ? proportional to the number of shirts sold.
is
is not
Answer:..
Step-by-step explanation: what is is not?
Answer:
1. is
2. amount raised, number of shirts sold
3. dependent, independent
4. 4
5. 4x
Step-by-step explanation:
you are in charge of buying the soda and paper plates for a party. The soda costs $3 per case and the paper plates cost $4 per stack. you have no more than $25 to spend.
The inequalities that define the given conditions are,[tex]4x+3y \leq25[/tex].Option A is correct.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given data;
Soda costs = $3 per case
Paper plates = $4 per stac
The maximum amount of money you can spend is $25
x = the number of cases of soda
y = the number of stacks of paper plates.
The inequalities that define the given conditions are;
[tex]4x+3y \leq25[/tex]
Hence, option A is correct.
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If [tex] \rm log_{3}( |5 - 2x| ) > 4[/tex] then x lies in interval of :
i)
[tex] ( - 43 \: , \: 38)[/tex]
ii)
[tex]( - \infty \: , \: 38 ) \cup(43 \: , \: \infty )[/tex]
iii)
[tex]( - 38 \: , \: 43)[/tex]
iv)
[tex]( - \infty \: , \: - 43) \cup(38 \: , \: \infty )[/tex]
[tex]\log_3|5-2x| > 4\\\log_3|5-2x| > \log_33^4\\|5-2x| > 3^4\\|5-2x| > 81\\5-2x > 81 \vee 5-2x < -81\\2x < -76 \vee 2x > 86\\x < -38 \vee x > 43\\x\in(-\infty,-38)\cup(43,\infty)[/tex]
Jej pls help i need my brother help
Answer:
[tex]\mathsf {\frac{17}{10}}[/tex]
Step-by-step explanation:
[tex]\mathsf {2\frac{2}{3} + \frac{14}{5} + ? = \frac{43}{6} }[/tex]
[tex]\mathsf {\frac{8}{3} + \frac{14}{5} + ? = \frac{43}{6} }[/tex]
Take the LCM (common denominator) to be 30.
[tex]\mathsf {\frac{80}{30} + \frac{84}{30} + ? = \frac{215}{30} }[/tex]
Bring the known values to the RHS.
[tex]\mathsf {? = \frac{215}{30} - \frac{164}{30} }[/tex]
[tex]\mathsf {? = \frac{51}{30}}[/tex]
[tex]\implies \mathsf {\frac{17}{10}}[/tex]
Let that be x
2 2/3=8/3Now
[tex]\\ \rm\rightarrowtail \dfrac{8}{3}+\dfrac{14}{5}+x=\dfrac{43}{6}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{40+42}{15}+x=\dfrac{43}{6}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{82}{15}+x=\dfrac{43}{6}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{43}{6}-\dfrac{82}{15}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{215-164}{30}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{51}{30}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{17}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=1\dfrac{7}{10}[/tex]
