Answer:
{a}p + 0.2m = 6
0.8m = 4
or 5p + m = 30
m = 5
{b} 5 lb peanuts and 5 lb mixture
Step-by-step explanation:
m1 → desired mixture with composition : 60% peanuts and 40% almonds and weight : 10 lb
⇒weight of peanuts in m1 = 60% × 5 = 6 lb
and weight of almonds in m1 is 4 lb
m2 → mixture with composition : 20% peanuts and 80% almonds and weight : m pounds
⇒weight of peanuts in m2 = 0.2m
and weight of almonds in m2 = 0.8m
p → weight (in pounds) of peanuts added to m2 to make m1
{a}
add p pounds of peanuts to m2 to make m1
equating weights of peanuts and almonds:
p + 0.2m = 6
0.8m = 4
{b}
equation gives m = [tex]\frac{4}{0.8}[/tex] ⇒ m = 5 lb
Using this in the [tex]1^{st}[/tex] equation:
p + 1 = 6 ⇒ p = 5 lb
Answer:
a) p + m = 10 and [tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex]
b) The mixing amount is 5 lb peanut and 5 lb mixture.
Step-by-step explanation:
Given that p pounds of peanuts and m pounds of the 80% almond and 20% peanut mixture are used to make 10 pounds of 60% peanuts and 40% of almonds mixture.
Now, we can write that p + m = 10 ........ (1)
Now, m pounds of 80% almond and 20% peanut mixture contain 0.2m pounds of peanuts and 0.8m pounds of almonds.
Now, from the condition given it can be written that
[tex]\frac{p + 0.2m}{0.8m} = \frac{60}{40}[/tex] .......... (2)
⇒ [tex]\frac{p + 0.2m}{0.8m} = \frac{3}{2}[/tex]
⇒ 2p + 0.4m = 2.4m
⇒ 2p = 2m
⇒ p = m
Now from equation (1) we get p = m = 5 pounds.
a) Therefore, equations (1) and (2) are the system of equations that models the situation.
b) The mixing amount is 5 lb peanut and 5 lb mixture. (Answer)
twinlakes on the shelf of a covenience store lose their fresh tastines over time. we say that the taste quality is 1 when the twinkies are first put on the shelf at the store, and that the quality of tastiness declined according to the function Q(t)=0.85^t. Graph this function on a graphing calculator, and determine when the taste will be half of its original value?
Answer:
The graph is shown below.
The time to make the taste to half is 4.265 s.
Step-by-step explanation:
Given:
Initial value of the taste is, [tex]Q_0=1[/tex]
Therefore, the quality of taste over time 't' is given as:
[tex]Q(t)=Q_0(0.85)^t\\Q(t)=1(0.85)^t[/tex]
Now, when the taste reduces to half, [tex]Q=0.5[/tex]
Therefore,
[tex]0.5=1(0.85)^t[/tex]
Taking natural log on both the sides, we get:
[tex]\ln(0.5)=\ln(0.85)^t\\\ln(0.5)=t\ln(0.85)\\t=\frac{ln(0.5)}{\ln(0.85)}=4.265\ s[/tex]
Therefore, the time to make the taste to half is 4.265 s.
So how am I supposed to get my.anwsers
You can look them up on here or other apps/websites.
A crane is lowering a concrete block from a height of 270 feet above the ground at a constant rate of 2.5 feet per second. Which function can be used to determine h, the height , in feet above the ground of the concrete block after “s” seconds ?
The function would be h = 270 - 2.5s, where h is the height (in feet) and s it the time (in seconds) that has passed.
The 270 represents the initial value, which is given. We are told that the initial height of the block is 270 feet.
2.5s represents the feet that it has descended. We know the block is lowered at a rate of 2.5 feet per second. Multiplying this by s, the time, will give us how much it has descended.
The height at any point is can be given by function f(s) = 270 - 2.5s.
Given to us,
concrete block top height, H = 270 feet,
speed of the block, v = 2.5 feet/second,
We know that [tex]\rm \bold{speed = \dfrac{Distance}{Time} }[/tex],
thus, [tex]\rm \bold{Distance = speed\times Time}[/tex]
So, we can write, height (distance from the top height) covered is "s" seconds as,
[tex]\bold{h = v \times s}=\bold{2.5\times s} = \rm \bold{2.5s}[/tex]
therefore, we can write,
Height at any point = Top height - height covered
= 270 - 2.5s
Hence, the height at any point is can be given by function f(s) = 270 - 2.5s.
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Ratio question. Someone please help me!
Answer:
b is the right answer
Step-by-step explanation:
because the ratio of 98÷10=9.8
when we did the ration of 1078÷110=9.8
we can say that both ratio is same.
Answer: [tex]\frac{98}{10}[/tex] ; x = 110
Step-by-step explanation:
Since the ratio of weight to mass is constant , it implies:
[tex]\frac{490}{50}[/tex] = [tex]\frac{1078}{x}[/tex]
490x = 1078 X 50
490x = 53900
x = 53900/490
x = 110
Therefore the ratio of weight to mass will be :
1078/110
98/10
Carter is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Carter will earn $50 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Carter earned a total of $1000 in royalties on 12 commercials and movies. Determine the number of commercials and the number of movies on which Carter's songs were played.
Answer:
Number of songs played in commercial are 7 and Number of songs played in movie are 5.
Step-by-step explanation:
Let Number of songs played in commercial be x
and Number of songs played in movie be y.
Total number of songs played =12
Hence,
[tex]x+y=12\ \ \ \ equation \ 1[/tex]
Also
Cost for songs played in commercial = $50
Cost for songs played in movie = $130
Total Money earned = $1000
Hence,
[tex]\$50x+\$130y=\$1000[/tex]
Dividing by 10 on both side we get;
[tex]\$5x+\$13y=\$100\ \ \ \ equation \ 2[/tex]
Now multiplying equation 1 by 5 we get;
[tex]5x+5y=60 \ \ \ \ equation \ 3[/tex]
Now Subtracting equation 3 from equation 2 we get;
[tex](5x+13y=100)- (5x+5y=60)\\8y=40\\y=\frac{40}{8}=5[/tex]
y = 5
x + y = 12
x + 5 = 12
x = 12 - 5
x = 7
Hence, Number of songs played in commercial are 7 and Number of songs played in movie are 5.
write an equation that is not a linear function explain why it is not linear
Answer:
x=y^2
Step-by-step explanation:
cause the definition of equation is one x correspond to one y,but one y can correspond to 2 x,
the picture I give to you a x correspond to 2 y
The function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
According to the question,
A nonlinear equation is given as,
y = x²
Now plotting the curve,
When we see that the relationship does not contain a straight line, and has a varying rate of change are nonlinear functions.
So this function is not linear.
Thus, the function that does not represent the straight curve and has a varying rate of change are nonlinear functions.
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Students were surveyed about their wither break plans.Of the people that stated they were going skiing, 25% did not actually go.How many students actually went skiing?
Answer:
The total number of students actually went for skiing is 0.75 times the total students .
Step-by-step explanation:
Given as :
Some Students were surveyed about their wither break plans.
The percentage of students who actually did not go for skiing = 25 %
So , The percentage of students who actually go for skiing = 100 % of students - 25 %
I.e The percentage of students who actually go for skiing = 75 %
Let The total number of students = x
So, out of x students , The The percentage of students who actually go for skiing = 75 % of the total students
I.e The The percentage of students who actually go for skiing = 75 % of x
Or, The The percentage of students who actually go for skiing = 0.75 × x
So, The number of students for skiing = 0.75 x
Hence The total number of students actually went for skiing is 0.75 times the total students . Answer
WRITE THE TERM,FILL IN THE BLANK
When we rewrite an expression so that it has no grouping symbols and all of the like terms have been combined, we ___ it.
Example: The process of turning (5x - 6) + 10x into 15x - 6.
The answer you’re looking for is: simplify.
When you rewrite an expression, we are simplifying it. We first use the distributive property through any groupings symbols, then evaluate terms we exponent that are given. Lastly, we combine any like terms, weather they are constants or variables.
Hope this helps! :)
Answer:
It is simplify. It is what you do when like terms are combined in order to get your answer.
Hope this helps!
F=9/5c+32 a is there a constant of proportionality? Explain your reasoning
yes because in a standard form that that equation is in, it'd be y=mx=b. the m represents the constant of proportionality or the rate of change. another name for it is the slope. in this case, the 9/5 is the m & c is x. meaning that, there is one & it is 9/5
Plato Question!!!!
Type the correct answer in each box.
What is a polar form of (-1, √3 ) is ( _ , _ ) ?
Answer:
(2, 120° )
Step-by-step explanation:
To convert from rectangular to polar form, that is
(x, y) → (r, Θ ), use
r = [tex]\sqrt{x^2+y^2}[/tex]
Θ = [tex]tan^{-1}[/tex]( [tex]\frac{y}{x}[/tex])
here (x, y ) = (- 1, [tex]\sqrt{3}[/tex])
r = [tex]\sqrt{(-1)^2+(\sqrt{3} }[/tex] )^2
= [tex]\sqrt{1+3}[/tex] = [tex]\sqrt{4}[/tex] = 2
Θ = [tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]) = 60° ← related acute angle
Note (- 1, [tex]\sqrt{3}[/tex]) is in the second quadrant so Θ must be in the second quadrant.
Θ = 180° - 60° = 120°
(- 1, [tex]\sqrt{3}[/tex]) → (2, 120°)
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
The polar form of a Cartesian coordinates is given by (r, @) where r = √x^2 + y^2
@ = tan^-1 y/x
r = √-1^2 + √3^2
r = √4
r= 2
@ = tan ^-1 √3/-1 -tan √3/1 = -60°
@ = 180-60 = 120°
A class has 4 boys and 10 girls. What is the ratio in simplest form that compares number of boys to total number of students?
4:14
4:10
2:7
2:5
Answer:
2:7
Step-by-step explanation:
There are 4 boys and 14 total students. That ratio is 4:14, and to find the simplest form you divide both numbers by the greatest common factor, which is 2. That leaves you with 2:7, the final answer.
Answer: simple just put boys=4ovrwhole class =14 put it in fraction 4/14 simplify you get 2/7
Step-by-step explanation:
The quadrilateral shown is a rhombus. If AB = 17 and AE = 8, what is the measure of BE
Answer:
[tex]BE=15\ units[/tex]
Step-by-step explanation:
we know that
In a rhombus the diagonals are perpendicular
so
The triangle ABE is a right triangle
see the attached figure to better understand the problem
Applying the Pythagoras Theorem to the right triangle ABE
[tex]AB^2=AE^2+BE^2[/tex]
where
AB is the hypotenuse of the right triangle (greater side)
AE and BE are the legs of the right triangle
we have
[tex]AB=17\ units\\AE=8\ units[/tex]
substitute
[tex]17^2=8^2+BE^2[/tex]
solve for BE
[tex]289=64+BE^2[/tex]
[tex]BE^2=289-64[/tex]
[tex]BE^2=225[/tex]
[tex]BE=15\ units[/tex]
Answer:
C) 16
Step-by-step explanation:
is this a function ?
Answer:
No
Step-by-step explanation:
For the relation to be a function
Each value of x from the domain ( values on left ) must map to exactly one unique value of y in the range ( values on the right )
Here x = 0 → 0 and 1 ( that is 2 values from the range )
Thus this does not represent a function
The mean of 20 observations is 50. If the observation 50 is replaced by 140, what will be the resulting mean?
Answer:
24.5
Step-by-step explanation:
20 + 140-50/20
= 20 + 4.5
=24.5
Which of the following equations is equivalent to y + 3 = -4(x - 2)?
Answer:
D. y= -4x +5
Step-by-step explanation:
The equation [tex]y+3=-4(x-2)[/tex] can be transformed by doing some algebra.If we solve the second term of the equation -4(x-2)= 8 - 4x, then we have [tex]y+3=8-4x[/tex] (this is done by distributing the multiplication into the two terms: remember that the product of -4x(-2)=+8 because the product of two negative numbers is a possitive number).Then, by subtracting both sides 3, we have [tex]y=5-4x[/tex]. Rearranging terms in the right side, we have [tex]y=-4x+5[/tex], which is option D.To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form.
Explanation:To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form. Here are the steps:
Distribute -4 to (x - 2): y + 3 = -4x + 8Move y to the right side: -4x + y + 3 = 8Combine like terms: -4x + y = 5Therefore, the equation that is equivalent to y + 3 = -4(x - 2) is -4x + y = 5.
use the rational exponent property to write an equivalent expression for
[tex] \sqrt[5]{n ^{4} } + 3 - 12[/tex]
Using the rational exponent property, an equivalent expression for[tex]\(x^{3/4}\[/tex] can be written as[tex]\(\sqrt[4]{x^3}\).[/tex]
Explanation:The rational exponent property states that for any real number a and positive integer[tex]\(n\), \(a^{m/n} = \sqrt[n]{a^m}\)[/tex] . Applying this property to the given expression[tex]\(x^{3/4}\[/tex] ), where (m = 3) and (n = 4), we can rewrite it as [tex]\(\sqrt[4]{x^3}\)[/tex] . This is derived by taking the fourth root of [tex]\(x^3\),[/tex] which is equivalent to raising [tex]\(x^3\)[/tex] to the power of[tex]\(1/4\).[/tex]
To further understand this, consider the original expression [tex]\(x^{3/4}\).[/tex] This represents the fourth root of [tex]\(x^3\)[/tex] , as the numerator 3 indicates the power to which x is raised, and the denominator 4 indicates the root. Expressing it as [tex]\(\sqrt[4]{x^3}\)[/tex] provides a clearer representation of the same mathematical concept, emphasizing the fourth root of [tex]\(x^3\).[/tex]
In mathematical notation, the rational exponent property is a useful tool for simplifying expressions involving fractional exponents. It allows us to transform expressions between radical form and exponent form, providing flexibility in mathematical manipulations and aiding in the understanding of the underlying concepts.
Round to the nearest tenth: 156.78
What is the equation of a line in slope intercept form that passes through the points (-4,3) and (-2,4)
Answer:
y=1/2x+5
Step-by-step explanation:
y-y/x-x for slope
4-3/-2-(-4) 1/2
Answer:
y= --2/4+5
Step-by-step explanation:
If I have a shirt that's 15 dollars how do I take 20% off the price
Well, first find out what 20% of $15 is.
20% x $15 = $3
Take that from the original price.
$15-$3=$12
Which of the following represents a geometric series
2+6+18
2,6,10
2+6+10+
2,6,18
good morning,
Answer:
2,6,18
Step-by-step explanation:
6/2=3 and 18/6=3 then 2,6,18 represent a geometric series.
6/2=3 and 10/6≠3 then 2,6,10 doesn’t represent a Géométric series.
:)
is (1 2) a solution of 6x-y>3
Answer:This can be checked by the following steps;
Step-by-step explanation:
The pair (1,2) is a solution to the inequality 6x - y > 3 because when these values are substituted into the inequality, the result is 4 > 3, which is a true statement.
Explanation:The question is asking if the pair of numbers (1,2) is a solution to the inequality 6x - y > 3. We can evaluate this by substituting the pair of values (1, 2) into the inequality in place of x and y. This gives us 6*1 - 2 > 3, or 6 - 2 > 3, which simplifies to 4 > 3. Since 4 is indeed greater than 3, we can conclude that the pair (1,2) is a solution to the inequality 6x - y > 3.
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: Create a story or context for this number sentence
50 1/2 divided by 1/4 + 202
Answer:
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
Step-by-step explanation:
Given:
[tex]\frac{50\frac{1}{2}}{\frac{1}{4}}+202[/tex]
The Story can be created as :
Tommy has 202 Chocolates with him in, his uncle gave him 50 1/2 bars of Chocolate each bar is further divided in 1/4 pieces to make 1 chocolate. Find the total number of Chocolates Tommy has?
on average a person blink 16 times per minute how many times does a person blink in one day. there are 1,440 minutes in a day
Answer:
16 times 1440= 23040 blinks a day
Step-by-step explanation:
So umm... 16 blinks a minute so for every minute is 16 blinks so just multiply the 1440 minutes so yeah..
What is the answer ?
Answer:
353
Step-by-step explanation:
355-42=x-40
I just need to subtract 2 from 355 to get x because I subtracted 2 from 42 to get 40.
355-2=353=x
3/10 11/12 5/8 in Oder from least to greatest
Answer: 5/8 11/12 3/10 I think
Step-by-step explanation:
Find common denominators (LCM is 120).
3/10 = 36/120
11/12 = 110/120
5/8 = 75/120
Now, we can put them from least to greatest.
3/10, 5/8, 11/12
______
Best Regards,
Wolfyy :)
could someone help with this inequality?
20≥−3.2(c−4.3)
thanks >o
The solution of inequality would be -
c ≥ 1.95
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
We have the following inequality -
20 ≥ −3.2(c − 4.3)
It is given that -
20 ≥ −3.2(c − 4.3)
−3.2(c − 4.3) ≤ 20
-3.2c + 13.76 ≤ 20
-3.2c ≤ 20 - 13.76
-3.2c ≤ 6.24
c ≥ 1.95
Therefore, the solution of inequality would be -
c ≥ 1.95
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Hello, i need help!
5/2 multiplied by what equals 1?
equation: 5/2×?=1
Answer:
[tex]\large\boxed{\dfrac{2}{5}}[/tex]
Step-by-step explanation:
[tex]\text{The product of the number and its reciprocal gives us 1.}\\\text{Reciprocal of }\ \dfrac{5}{2}\ \text{is equal}\ \dfrac{2}{5}.\\\\\dfrac{5}{2}\times\dfrac{2}{5}=\dfrac{5\!\!\!\!\diagup}{2\!\!\!\!\diagup}\times\dfrac{2\!\!\!\!\diagup}{5\!\!\!\!\diagup}=\dfrac{1}{1}\times\dfrac{1}{1}=1\times1=1[/tex]
Mathematical
PRACTICE 5 Use Math Tools Sarah buys a pen that costs
$0.75. How much will 2 pens cost?
Answer: 1.5
Step-by-step explanation:
0.72 • 2 = 1.5
Answer:1.50
Step-by-step explanation: 75•2 = 1.50
last year, Mr. Petersen's rectangular garden had a width of 5 meters and an area of 20 square meters.
This year, he wants to make the garden three times as long and two times as wide.
a
Solve for the length of last year's garden using the area formula. Then, draw and label the
measurements of this year's garden
Last Year
This Year
20
square
meters
Answer:
Last year: length of 4 meters
This year: width of 10 meters and a length of 12 meters
Step-by-step explanation:
The variables y and x have a proportional relationship, and y = 7 when x = 2.
What is the value of y when x = 5?
Enter your answer in the box.
y = 17.5 when x = 5
Step-by-step explanation:
When two variables are in direct proportion i.e. change in one variable causes change in other variable it can be expressed mathematically as:
y∝x
when the proportionality symbol is removed a proportionality constant is introduced
So,
[tex]y = kx[/tex]
Putting y = 7 and x = 2
[tex]7 = k * 2\\k = \frac{7}{2}\\k = 3.5[/tex]
So the expression will be:
[tex]y = 3.5x[/tex]
Now putting x = 5
[tex]y = 3.5 * 5\\y = 17.5[/tex]
Hence,
y = 17.5 when x = 5
Keywords: Proportion, variables
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