The ratio of blue paints to yellow paint is a mixture of 2 : 3.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
The Total cans of blue paint = 14
Total cans of yellow paint = 20
Day 1:
Yellow paint = 6 cans
Blue paint = 4 cans
The ratio of blue paints to yellow paint
= 2 : 3
Day 2:
Yellow paint = 9 cans
Blue paint = 6 cans
The ratio of blue paints to yellow paint
2 : 3
Day 3:
Cans of yellow remaining after 2 days
Yellow paint = Total cans of yellow paint - day 1 cans of yellow paint - day 2 cans of yellow paint
= 20 - 6 - 9
= 20 - 15
= 5 cans
Cans of blue remaining after 2 days
Blue paint = Total cans of blue paint - day 1 cans of blue paint - day 2 cans of blue paint
= 14 - 4 - 6
= 14 - 10
= 4 cans
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When determining how well an observed set of frequencies fits an expected set of frequencies, what is the test statistic
Answer: [tex]\chi^2[/tex] test statistic.
Step-by-step explanation:
The chi-square ([tex]\chi^2[/tex] ) test is a non-parametric statistical test(also known as Goodness of fit test) which is used to determine if a distribution of observed frequencies differs from the expected frequencies.
Chi-square statistic uses either nominal (categorical) or ordinal level data.
Hence, When determining how well an observed set of frequencies fits an expected set of frequencies, the test statistic is [tex]\chi^2[/tex] test statistic.
simplify the expression. -2 3/5 - (-1 2/5) - 4/5 = ?
What is the value of 2 over 5×5ovet4÷2over3
Answer:
3/4
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by its reciprocal.
[tex]\dfrac{2}{5}\times\dfrac{5}{4}\div\dfrac{2}{3}=\dfrac{2}{5}\times\dfrac{5}{4}\times\dfrac{3}{2}\\\\=\dfrac{(2)(5)(3)}{(2)(5)(4)}=\boxed{\dfrac{3}{4}}[/tex]
Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron. What position, in microns, are 20% of binding sites greater than
Answer:
2.74 microns
Step-by-step explanation:
According to the given situation, the calculation of position, in microns, is shown below:-
Here we will use the standard normal table,
P(Z > z) = 20%
1 - P(Z < z) = 0.2
P(Z < z) = 1 - 0.2
P(Z < 0.84) = 0.8
after solving the above equation we will get
z = 0.84
Now we will use the z-score formula,
[tex]x = z \times \sigma + \mu[/tex]
[tex]x = 0.84 \times 0.35 + 2.45[/tex]
x = 0.294 + 2.45
= 2.744 microns
or
= 2.74 microns
Ashanti and Maria went to the store to buy snacks for their back-to-school party. They bought bags of chips, pretzels, and nachos. They bought three times as many bags of pretzels as bags of chips, and two fewer bags of nachos than bags of pretzels. If x represents the number of bags of chips they bought, express, in terms of x, how many bags of snacks they bought in all.
(Theres two more problems in a picture, you don’t have to answer all three tho but if you do it i will love you forever :( )
Answer:
Hey there!
For the first one:
Chips: x
Pretzels: 3x
Nachos: 3x-2
Total snacks: x+3x+3x-2=7x-2
For the second one:
In the equation, 150+5d, 150 represents the starting amount of money, in this case, 150 dollars. 5d means that for every day, five dollars get put into his account.
For the third one:
In this equation, 1.50 represents to initial fee, and 2.25m represents the cost per mile. Dividing by 2 gives us what each person in the cab pays.
Let me know if this helps :)
Use Theorem to find ℒ{f(t)}.
f(t) = (et − e−t)2
Answer:
[tex]\frac{3s^2-4}{s(s^2-4)}[/tex]
Step-by-step explanation:
Here, the question is to find the Laplace transformation of [tex]f(t)[/tex]
where, [tex]f(t)=(e^t-e^{-t})^2[/tex]
We know that for [tex]t>0[/tex], [tex]\mathcal{L}\{f(t)\} =\int_0^{\infty} e^{-st}f(t)dt[/tex]
[tex]\mathcal{L}\{e^{at}\}=\int_0^{\infty} e^{-st}e^{at}dt[/tex]
[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\int_0^{\infty} e^{(a-s)t}dt[/tex]
[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\left[\frac { e^{(a-s)}}{a-s}\right]_0^{\infty}[/tex]
[tex]\Rightarrow \mathcal{L}\{e^{at}\}=\frac { 1}{s-a}\cdots(i)[/tex]
Here, we have [tex]f(t)=(e^t-e^{-t})^2[/tex]
[tex]\Rightarrow f(t)=(e^t)^2+(e^{-t})^2-2(e^t)(e^{-t})[/tex]
[tex]\Rightarrow f(t)=e^{2t}+e^{-2t}-2e^{0t}[/tex]
So, the laplace transformation of [tex]f(t)[/tex] is
[tex]\mathcal{L}\{f(t)\}=\mathcal{L}\{e^{2t}+e^{-2t}-2e^{0t}\}[/tex]
[tex]\Rightarrow \mathcal{L}\{f(t)\}=\mathcal{L}\{e^{2t}\}+\mathcal{L}\{e^{-2t}\}+\mathcal{L}\{e^{0}\}[/tex]
Now, using equation[tex](i)[/tex]
[tex]\mathcal{L}\{f(t)\}=\frac{1}{s-2}+\frac{1}{s-(-2)}+\frac{1}{s-0}[/tex]
[tex]\Rightarrow \mathcal{L}\{f(t)\}=\frac{1}{s-2}+\frac{1}{s+2}+\frac{1}{s}[/tex]
[tex]\Rightarrow \mathcal{L}\{f(t)\}=\frac{3s^2-4}{s(s^2-4)}[/tex]
Hence, the Lapelace transformation of [tex]f(t)=(e^t-e^{-t})^2[/tex] is
[tex]\frac{3s^2-4}{s(s^2-4)}[/tex].
What are the intercepts of y = x + 5 (Remember that intercepts mean both x-intercept & y-intercept.) a) (5, 0) & ( 0, 5) b) ( -5, 0) & (0 , 5) c) (5, 0 ) & (0, -5) d) (-5, 0 ) & ( 0, -5)
Greetings from Brasil...
We have to remember 2 details:
→ When X = 0, the function intersects the Y axis
→ When Y = 0, the function intersects the X axis
So
1: X = 0
Y = X + 5
Y = 0 + 5
Y = 5
X = 0 and Y = 5 ⇔ (0; 5)
2: Y = 0
Y = X + 5
0 = X + 5
X = - 5
Y = 0 and X = - 5 ⇔ (- 5; 0)
Then the point at which the graph intersects the X and Y axis will be
(0; 5) and (- 5; 0)
What is the probability of choosing a card from a deck of cards that is a club or a ten? Is this event mutually
exclusive or inclusive?
A. Inclusive
B. Exclusive
A. 5/16
B. 4/13
C. 1/4
D. 7/16
Answer:
Hey there!
There are 13 clubs in a deck of cards.
There are 4 tens.
However, the tens overlap with the clubs, so there are 16 cards to choose.
16/52=4/13
Let me know if this helps :)
The events are mutually inclusive. Option B is correct because the required probability is [tex]\dfrac{4}{13}[/tex].
Important information:
A card is selected randomly from a deck of cards.We need to find the probability that the card is a club or a ten.Probability:A deck of cards has total 52 cards, which includes 4 suits and each suit has 13 cards. If S be the sample space, then n(S) = 52.
Let A be the event that the card is a club card and B be the event that it is a ten card.
The number of club cards is 13. So, n(A) = 13.
There are 4 cards of 10. So, n(B) = 4.
One ten card is of club. So, [tex]n(A\cap B)=1[/tex].
Since [tex]n(A\cap B)=1\neq 0[/tex], therefore the events are mutually inclusive.
The number of club or a ten card is:
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
[tex]n(A\cup B)=13+4-1[/tex]
[tex]n(A\cup B)=16[/tex]
Now,
[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]
[tex]P(A\cup B)=\dfrac{16}{52}[/tex]
[tex]P(A\cup B)=\dfrac{4}{13}[/tex]
Therefore, the probability of choosing a card from a deck of cards that is a club or a ten is [tex]\dfrac{4}{13}[/tex]. Hence, option B is correct.
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What is the absolute value of -4
Answer:
4
Step-by-step explanation:
Easiest way to remember absolute value is the number always comes out positive.
l-4l=4
Answer:
the answer is 4
Step-by-step explanation:
the absolute value means it doesn't consists of any sign (neither positive nor negative)
Let p: x = 4 Let q: y = -2 Which represents if x = 4, then y = -2. Please hurry
Answer:
p: x = 4
q: y = -2
If p happens then q will also happen
Step-by-step explanation:
Given two propositions, we want to rearrange them in a conditional statement.
The correct answer is:
p → q
First, a conditional statement is something of the form:
If [Hypothesis] then [Conclusion]
So, if the first part is true, then the second part must be true.
Now, here we have two propositions:
p: "x = 4"
q: "y = -2"
We want to write:
"if x = 4, then y = -2"
this is just written as: "p implies q" or:
p → q
Where "→" means "then", and the initial "if" is tacit.
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What is lim x → 9+ ( x - 9/| 9 - x | )
Answer:
The answer is nonexistent
Step-by-step explanation:
Question 3: A small window in a barn is shaped like a parallelogram. The height of the window is half the length of the base of the window. The base of the window is 12 in. The length of the other side of the window is 10 in. What is the area of the window? A) 22 B) 60 C) 72 D) 120
Answer:
The answer is B (60)
Step-by-step explanation:
The formula for area is L x W, since they claim the base is 12in and even state teh length is 10in all that is needed is to multiply 12 x 10 to get 120. The area of the window is 120 inches. and half of 120 is 60 Area articulates the space occupied by a flat shape or the surface of an object. The answer is B
The area of the window will be 60 square inches. Then the correct option is B.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.
A small window in a barn is shaped like a parallelogram. The height of the window is half the length of the base of the window.
The formula for area is L x W, since they claim the base is 12in and even state the length is 10 in all that is needed is to multiply 12 x 10 to get 120.
The area of the window is 120 inches and half of 120 is 60 Area articulates the space occupied by a flat shape or the surface of an object.
The area of the window will be 60 square inches. Then the correct option is B.
More about the parallelogram link is given below.
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Hugh is struggling in his history class. His last five grades on tests were 67, 72, 63, 77, and 59. On the next test, he studies hard, but gets a 75. What is his average?
Answer:
Step-by-step explanation:
[tex]\frac{67+72+63+77+59+75}{6} \\\\\frac{413}{6} \\\\68.833333 or 68.8[/tex]
The solution to an inequality is represented by the number line. A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5. How can this same solution be written using set-builder notation?
Answer:
3
Step-by-step explanation:
The number line is showing x>3.
If the circle were closed it would be x≥3.
Answer:
3.
Step-by-step explanation:
For the equation 17h+6=40, select the appropriate property of equality to move the constant term to the right side of the equation.(20pt) A. Division Property of Equality- B. Subtraction Property of Equality - C. Multiplication Property of Equality- D. Addition Property of Equality
Answer:
Option B.
Step-by-step explanation:
The given equation is
[tex]17h+6=40[/tex]
We need to find the property of equality to move the constant term to the right side of the equation.
In the given equation 6 is the constant term on the left side.
Using subtraction property of equality, subtract 6 from both sides.
[tex]17h+6-6=40-6[/tex]
[tex]17h=34[/tex]
So, the appropriate property of equality to move the constant term to the right side of the equation is Subtraction Property of Equality.
Therefore, the correct option is B.
The area of a rectangular wall of a barn is 48 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.
l = 16 feet
w = 3 feet
Step-by-step explanation:A = l×w
l = 10+2w
48 = (10 + 2w)w
48 = 10w + 2w² | : 2
24 = 5w + w²
w² + 5w - 24 = 0
w² + 8w - 3w - 24 = 0
w(w + 8) - 3(w + 8) = 0
(w - 3)(w + 8) = 0
w - 3 = 0 => w = 3 feet
w + 8 = 0 => w = - 8 ∉ N
l = 10 + 2w
l = 10 + 6
l = 16 feet
A = l×w = 16ft×3ft = 48ft²
If speed varies inversely as the time it takes to drive and Kris takes 5 hours driving at 55 mph, what speed will Martin need to
drive if he wants to take 5 hours?
O 50 mph
52.4 mph
O 60.5 mph
O 51.5 mph
Answer:
55mph . None of the options are correct
Step-by-step explanation:
If the speed varies inversely as the time it takes to drive, then v ∝ 1/t. where;
v is the speed
t is the time taken
Hence;
v = k/t with k being the constant of proportionality.
Since it takes Kris 5 hours when driving at 55 mph, we will substitute v = 55mph and t = 5 hours. into the equation above to get the value of k as shown:
55 = k/5
Cross multiply
k = 55*5
k = 275
Hence, to calculate the speed it will Martin to drive for 5 hours, we will substitute k = 275 and t = 5 into the original equation v = k/t as shownl
v = 275/5
v = 55 mph
Hence, we can conclude that Martin will also need to drive at a speed of 55mph if he wants to take 5hours.
HELP !! a sandwich shop purchases a used pizza oven for $875. after 5 years, the oven will have to be discarded and replaced. write a linear equation giving the value V of the equipment during the 5 years it will be in use.
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Explanation:
I'll use y in place of V for now. Also, I'll use x in place of t.
x = number of years
y = value of the oven
Initially, the oven's value is $875, so x = 0 and y = 875 pair up together. The point (0,875) is on the line.
The point (5, 0) is also on the line to indicate that x = 5 years later is when the value of the oven is y = 0 dollars.
We need to find the equation of the line through (0,875) and (5,0)
First we'll need the slope
m = (y2-y1)/(x2-x1)
m = (0-875)/(5-0)
m = -175
The negative slope means the oven is losing 175 dollars in value each year.
The y intercept is b = 875 as this is the initial value of the oven
Put together, y = mx+b turns into y = -175x+875
If we plugged x = 0 into this equation, we'd get y = 875
Similarly, plugging x = 5 into y = -175x+875 leads to y = 0. This helps check we have the right equation
Lastly, replace x with t and replace y with V to end up with V = -175t + 875 which is our final answer.
Evaluate the expression |3x – 1| for x = -2.
A. -7
B. 7
C. 5
D. -5
Answer:
B. 7
Step-by-step explanation:
|3x – 1| =
= |3(-2) - 1|
= |-6 - 1|
= |-7|
= 7
Answer: B. 7
Please! Help! BRAINLEST!!!
Hi there! Hopefully this helps!
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Answer: [tex]v = 8[/tex]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]12 = 12+ \frac{v-8}{2}[/tex]
Multiply both sides of the equation by 2 to get:
[tex]24 = 24 + v - 8[/tex]
Subtract 8 from 24 to get 16.
[tex]24 = 16 + v[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]16 + v = 24[/tex]
Subtract 16 from both sides.
[tex]v = 24 - 16[/tex]
Subtract 16 from 24 to get, you guessed it, 8!Was it evaluated correctly?
Explain your reasoning
Janet wants to calculate the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest. What equation can she use?
Answer:
T = 100I/PRStep-by-step explanation:
Given the amount invested for a particular period of time at an interest rate, the equation that can model the Interest achieved on investment is expressed using the simple interest formula as shown;
Simple Interest = PRT/100 where;
P is the principal (amount invested)
R is the rate (in %)
T is the time (in years)
From the equation I = PRT/100, we need to express tht time T as a function of the rest of the variable as shown;
I = PRT/100
cross multiply
100I = PRT
Divide both sides by PR
100I/PR = PRT/PR
100I/PR = T
Hence the the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest is expressed as
T = 100I/PR
How can you use a rectangle to calculate the slope of a line ?
Answer:
The slope is the inclination of a surface or a line with respect to the horizontal. It can be measured at an angle in degrees, radians or grades or even in percentage, that is to say according to the height to length ratio multiplied by 100.
Step-by-step explanation:
BRAINLIEST FOR RIGHT ANSWER!!! The graph shows two lines, A and B. (IMAGE BELOW) How many solutions are there for the pair of equations for lines A and B? Explain your answer.
Answer:
1 solution; (1,4)
Step-by-step explanation:
Whenever two lines intersect, their solution is the point that the two share in common. Here, it's (1,4), so that is the answer.
After a filling meal, Ms. Ironperson and Mr. Thoro went their separate directions. Ms. Ironperson lives due east from the Shawarma Mediterranean Grill and Mr. Thoro lives due south. Both leave at the same time; Ms. Ironperson traveling at 50 mph and Mr. Thoro at 60 mph. If Ms. Ironperson travels at rate of 50t and Mr. Thoro travels at a rate of 60t, what is the correct equation to find how long it will take them to be 400 miles apart?
Options :
A) 50t + 60t =4002
B) (50t)2+(60t)2 = 4002
C) 50t + 60t = 400
C) 50t2 + 60t2 = 4002
Answer:
400^2 = (50*t)^2 + (60*t)^2
Step-by-step explanation:
Given the following :
Ms. Ironperson:
moves due east
Speed = 50 mph
Rate of travel = 50t
Let time taken = t ; hence Distance covered with respect to time = ( 50 * t) = 50t
Mr. Thoro
moves due South
Speed = 60 mph
Rate of travel = 60t
Let time taken = t ; hence Distance covered with respect to time = ( 60 * t) = 50t
They are moving at right angle from each other, thus, we can apply Pythagoras rule ;
The displacement between them will be = 400 miles which is the hypotenus
From Pythagoras :
Hypotenus^2 = opposite^2 + Adjacent^2
Displacement = distance 1 + distance 2
400^2 = (50*t)^2 + (60*t)^2
Determine the value of x shown in the diagram
Answer:
x = 145
Step-by-step explanation:
If we look at the right triangle with sides of 24 and 30, we can find the missing leg using the Pythagorean Theorem. If we look carefully, we notice that 18:24:30 is basically the 3:4:5 Pythagorean Triple multiplied by 6, so the missing side is 18. If we look at the right triangle with sides of x and 24, we can find the missing side by calculating 161 - 18 = 143. Using the Pythagorean Theorem, we know that 143² + 24² = x² so x = 145.
PLEASE HELP *13 POINTS*! A) -4 B) -0.25 C) 4 D) 0.25
Answer: Choice C) 4
=========================================
Work Shown:
Set the denominator equal to zero and solve for x
4x-16 = 0
4x-16+16 = 0+16 ... add 16 to both sides
4x = 16
4x/4 = 16/4 ... divide both sides by 4
x = 4
--------
If x = 4, then the denominator is 0
4x-16 = 4(4)-16 = 16-16 = 0
So this x value is what we exclude from the domain to avoid a division by zero error.
What is the solution for x in the equation? 16x − 4 + 5x = -67
Answer:
x = -3
Step-by-step explanation:
16x − 4 + 5x = -67
Combine like terms
21x -4 = -67
Add 4 to each side
21x-4+4 = -67+4
21x = -63
Divide each side by 21
21x/21 = -63/21
x = -3
Answer:
[tex]\huge \boxed{x = -3}[/tex]
Step-by-step explanation:
[tex]16x - 4 + 5x = -67[/tex]
Combine like terms.
[tex]21x - 4 = -67[/tex]
Add 4 to both sides.
[tex]21x = -63[/tex]
Divide both sides by 21.
[tex]x = -3[/tex]
(5 points) The probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%. What is the probability that a randomly selected day in April will be rainy or windy?
Answer:
The probability that a randomly selected day in April will be rainy or windy is 0.62 or 62%.
Step-by-step explanation:
We are given that the probability of rain on any day in the month of April is 34%. The probability that it will be windy on any day in the month of April is 38%, and the probability of both is 10%.
And we have to find the probability that a randomly selected day in April will be rainy or windy.
Let the probability of rain on any day in the month of April = P(A) = 0.34
The probability of windy on any day in the month of April = P(W) = 0.38
The probability of both windy and rainy on any day in the month of April = P(R [tex]\bigcap[/tex] W) = 0.10
Now, the probability that a randomly selected day in April will be rainy or windy is given by = P(R [tex]\bigcup[/tex] W)
P(R [tex]\bigcup[/tex] W) = P(R) + P(W) - P(R [tex]\bigcap[/tex] W)
= 0.34 + 0.38 - 0.10
= 0.62 or 62%
So, the probability that a randomly selected day in April will be rainy or windy is 62%.
Solve for q 10/9=3/q q=
Answer:
q = 27/10
Step-by-step explanation:
10/9 = 3/q
To find q, we must seperate it from the other numbers,
First we divide both sides by 3,
(10/9)/3 = (3/q)/3
10/27 = 1/q
Now we find the reciprocal of both sides to get the answer,
27/10 = q
q = 27/10