Yes!, This is a proportional relationship.
A proportional relationship means that the ratios of two variables are equal.
According to the question, the requirements of the recipe are
Number of cups of sour cream required be x1 = 4
Number of packages of onion soup mix required be y1 = 3
Used products by Harlan,
Cups used by Harlan of sour cream be x2 = 2
Packages of onion soup mix used by Harlan be y2 = 1.5
As we can see that,
x1/x2 = y1/y2
4/2 = 3/1.5
2 = 2
L.H.S = R.H.S ( ratio is same)
Therefore, we conclude that the above case is a proportional relationship.
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Find an equation of the form f(x)=ax^2+bx+c. must solve algebraically and check using a calculator (state, the steps used to perform the check).
f(1)=4, f(2)=13, f(4)=46
The equation of the form [tex]f(x)=ax^2+bx+c[/tex] that must solve algebraically and f(1)=4, f(2)=13 and, f(4)=46 is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].
Putting x = 1 in the given equation, we get
[tex]f(1)=a(1)^2+b(1)+c[/tex]
f(1) = a + b + c = 4 ...(1)
Putting x = 2 in the given equation, we get
[tex]f(2)=a(2)^2+b(2)+c[/tex]
f(2) = 4a + 2b + c = 13 ...(2)
Putting x = 4 in the given equation, we get
[tex]f(4)=a(4)^2+b(4)+c[/tex]
f(4) = 16a + 4b + c = 46 ...(3)
Using elimination method to solve the set of linear equations, we get
(2) - (1), we get
3a + b = 9 ...(4)
(3) - (2), we get
12a + 2b = 33 ...(5)
Multiplying (4) by 2, we get
6a + 2b = 18 ...(6)
(5) - (6), we get
6a = 15
a = 15/6 = 5/2
Putting a = 5/2 in (4), we get
3(5/2) + b = 9
15/2 + b = 18/2
b = 3/2
Putting the values of a and b in (1), we get
5/2 + 3/2 + c = 9
4 + c = 9
c = 9 - 4
c = 5
Hence, the equation is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].
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what is the constant of prportionality in the equation y= 5x
The constant of proportionality on the equation is 5.
What is constant of proportionality?
Constant of proportionality is defined as the ratio that relates two given value. When two values are directly or indirectly proportional to one another, there relation is expressed as y = kx.
We compare the general direct proportionality relation with the equation given.
The equation given : y = 5x
The direct relationship between y and x is :
y α x
y = kx - - - (1)
Where, y and x are variables and k is the constant of proportionality.
Comparing equation (1) with the equation given :
y = kx
y = 5x
We can observe that, k in the equation (1) equals to 5 in the given equation.
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The area of a rectangular living room is 450 square feet. The length of the room is 15 feet less than three times the width.
The length of the rectangle is 30 feet and the width of the rectangle is 15 feet.
Let l be the length l the rectangle and w be the width of the rectangle.
The area of a rectangular living room is 450 square feet.
⇒ A = l × w
⇒ 450 = l × w ................(1)
The length of the room is 15 feet less than three times the width.
So we get an expression,
l = 3w - 15
Substitute above vale of l in equation (1)
450 = (3w - 15) × w
450 = 3w² - 15w
3w² - 15w - 450 = 0
w² - 5w - 150 = 0
(w - 15)(w + 10) = 0
w - 15 = 0 or w + 10 = 0
w = 15 or w = -10
But width of the rectangle cannot be -10
So, w = 15 feet
and l = 3(15) - 15
l = 30 feet
Therefore, the length of the rectangular living room is 30 feet and the width is 15 feet.
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A normal distribution has a mean of u = 60 and a standard deviation of o = 18. For each of the follow-
ing samples, compute the z-score for the sample mean
and determine whether the sample mean is a typical,
representative value or an extreme value for a sample
of this size.
a. M= 67 for n = 4 scores
b. M = 67 for n = = 36 scores
Answer:
HI
Step-by-step explanation:
HOW ARE
Help me Plss is very hard and i need an answer
Line C has the constant of proportionality between y and x of 2/3.
What is defined by constant of proportionality?The proportionality constant is the constant value of the ratio of two proportional quantities. When the ratio or product of two varying quantities yields a constant, they are said to be in a proportional relationship.For the given question;
Constant of proportionality = change in y / change in x
Check for each line;
Line A; select any coordinate from the graph.
(7, 3); Put in the formula
Constant of proportionality = 7/3
Thus, Line A has Constant of proportionality between y and x of 7/3.
Line B; select any coordinate from the graph.
(4, 3); Put in the formula
Constant of proportionality = 4/3
Thus, Line B has Constant of proportionality between y and x of 4/3.
Line C; select any coordinate from the graph.
(2, 3); Put in the formula
Constant of proportionality = 2/3
Thus, Line C has Constant of proportionality between y and x of 2/3.
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Be Precise An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees. Write each ratio in three ways.
Ratio in three ways are given below.
What is ratio?The ratio is the number that can be used to represent one quantity as a percentage of another, to put it simply. A ratio's two numbers can only be compared if they share the same unit. Ratios are used to compare two objects. a connection between two values that is typically expressed as the quotient of one value divided by the other. For instance, the ratio of red to blue marbles is 6:4, or six red to four blue marbles, in the case of a box containing six red and four blue marbles. A decimal or percentage can also be used to indicate a ratio.
Given Data
An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees.
a) Rows of Gala apple trees to Granny apple smith trees:
Ratio
First way = 15 to 12
Second way = 15:12
Third way = [tex]\frac{15}{12}[/tex]
b) Rows of Fuji apple trees to total number of apple trees
Total number = 12 + 10 + 15 + 2 +2
Total number = 41
Rows of Fuji apple trees = 10
First way = 10 to 41
Second way = 10: 41
Third way = [tex]\frac{10}{41}[/tex]
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AO. Use the appropriate divisibility rule to determine which of the following numbers is a factor of
315438530. (In each case, state "Yes" or "No" and explain briefly your use of the rule.)
(i) 2, (ii) 3, (iii) 4, (iv) 5, (v) 6, (vi) 8, (vii) 11
The results based on divisibility rules are given below -
What are divisibility rules?A divisibility rule is a convenient shorthand for checking if an integer is divisible by a given set divisor without actually doing the division, typically by looking at the digits of the number.
Rule of Divisibility for 2: The given integer's final/unit digit must be an even number or a multiple of two, i.e., 0, 2, 4, 6, and 8.
Dividend Rule for Number 5: The provided number should have a unit digit of 0 or 5.
Yes, As number on ones place is multiple of 2.No, as the sum of numbers is not divisible by 3.No, As numbers on tens place are not divisible by 4.Yes, As number on ones place is 0.No, As the number is divisible by 2 but not 3.No, As number on hundreds place is not divisible by 8.Yes, using even odd method.To learn more about divisibility rules from given link
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Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours.
How long will it take them to finish the job together?
Answer:
use keywords together. So I think all you have to do is multiply or add them both together. Try multiplying or adding but I know that those are part of the answer.
Step-by-step explanation:
A 75 -inch pipe is cut into two pieces. One piece is two times the length of the other. Find the lengths of the two pieces.
Answer:
5 times the length of the short piece = 75 inches
The length of the short piece =75 / 5 = 15 inches
Length of the long piece = 4 times the length of the short piece = 60 inches
Check: 15 + 60 = 75 inches
yay
What is the value of the expression -83 + (-56)
helppppp. can you help please?
P (-5), replace x by (-5).
[tex]p(x)=8(-5)^4+39(-5)^3-n(-5)^2+6(-5)-20[/tex]Solve the parentheses:
[tex]p(x)=8(625)+39(-125)-n(25)-30-20[/tex][tex]p(x)=5,000-4,875-25n-30-20[/tex]Combine like terms:
[tex]p(-5)=75-25n[/tex]The measures of the exterior angles of a triangle are 5x°, 9x°, and 10x°. Find the
measure of the largest exterior angle.
The measure of largest exterior angles is 150 degrees
What are exterior angles?Exterior angles are defined as angles of a polygon formed or created by two the sides of that polygon and sharing a common endpoint.
It is important to note that the exterior angle of a triangle is congruent to the sum of the two non-adjacent interior angles that are opposite to each other.
They are also known to be angles formed by a transversal line as it cuts through one of two lines and it is located on the outside part of the line.
Given the angles as;
5x°9x°10x°Note that the sum of exterior angles are 360degrees
5x° + 9x° + 10x° = 360°
collect like terms
24x = 360
Make 'x' the subject of formula by dividing both sides by 24
x = 360/24
x = 15
But the largest angle is 10x = 10(15) = 150°
Hence, the value is 150°
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All changes savedFor the three-part question that follows, provide your answer to each question in the given workspace.Identify each part with a coordinating response. Be sure to clearly label each part of your response asPart A, Part B, and Part C.A bag contains three blue marbles, five red marbles, and four green marbles.Part A: What is the probability of selecting a red marble?Part B: What is the probability of selecting three red marbles without replacement?Part C: In a short paragraph, explain in your own words your work to Step B.
If there are three blue marbles, five red marbles, and four green marbles, the probability of selecting a red marble is
[tex]P=\frac{5}{3+5+4}=\frac{5}{12}_{}[/tex]Remember that the probability is the ratio between the number of events and the total number of all the events. In this case, the number of events is 5 because there are 5 red marbles, and the total number of all events is the sum of all the marbles.
Therefore, the probability of selecting red marbles is 5/12.
Part B.[tex]P=\frac{5}{12}\cdot\frac{4}{11}\cdot\frac{3}{10}=\frac{5\cdot4\cdot3}{12\cdot11\cdot10}=\frac{60}{1320}=\frac{30}{66}=\frac{15}{33}[/tex]Notice that we have three different ratios, that is because each time we select a red marble it represents a different situation since we won't place back the red marble into the bag, that's why each event decreases by one and each denominator too.
Therefore, the probability of selecting three red marbles without replacement is 15/33.
Part C.As we said before, in Part B, we had to multiply each probability for each time we select a red marble. It's important to notice that the numerators decreased by 1 (5,4,3) because each time we select a marble we won't place it back, that's the reason why the denominator also decreased by 1.
A probability experiment consists of rolling a fair 15-sided die. Find the probability of the event below. rolling a number divisible by 3
Probability of an experiment consists of rolling a fair 15 -sided die with an event of rolling a number divisible by 3 is P(E)=(1 /3).
As given ,
Total number of outcomes of an experiment consists of rolling a fair 15-sided die 'n'
={1, 2, 3, …., 14, 15}
=15
Number of outcomes of an event 'E' showing rolling a number divisible by 3 'n(E)'
={3,6,9,12,15}
=5
Probability of event showing rolling a number divisible by 3 'P(E)'
=(Total number of favourable outcomes)/(Total number of outcomes)
=n(E)/n
= 5/15
=1/3
Therefore, probability of an experiment consists of rolling a fair 15 -sided die with an event of rolling a number divisible by 3 is P(E)=(1 /3).
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Simplify (write without the absolute value sign) :
Problem 1 : |5-x|-|x+8|, if x>5
Problem 2 : |x − 2| + |8 − x| + 2, if 2 ≤ x < 8
Problem 3 : |x − 5| − |2 − x| + |x + 1|, if x ≥ 5
Problem 4 : |7 − x| + |4 − 2x| − |x − 8, if x < 2
Simplification of the given problems without absolute value sign:
1. |5-x|-|x+8|, if x>5 is equal to -13.
2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.
3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.
4. |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.
As given,
Simplification of the given problems without absolute value sign:
1. |5-x|-|x+8|, if x>5
= x - 5-(x+8)
= x-5 -x-8
= -13
2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8
= x -2+ 8 -x+2
=8
3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5
= x-5-(x-2)+(x+1)
=x-5-x+2+x+1
=x-2
4. |7 − x| + |4 − 2x| − |x − 8, if x < 2
= 7-x +4-2x-8 +x
=3-2x
Therefore, simplification of the given problems without absolute value sign:
1. |5-x|-|x+8|, if x>5 is equal to -13.
2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.
3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.
4. |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.
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7 Describe the error in solving the equation
(1) 3 (X + 4) = 13
(2) 3x + 4 =13
(3) 3 x = 9
(14)X = 3
the error in the equation is 3 is not multiplied by 4 which gives wrong value of x .
What is the linear equation ?A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. Finding both the intercepts of an equation in this way is quite easy (x and y).
Calculation3 (x + 4) = 13
3x + 12 = 13 \\the place where the error was occurred in the question\\
3x = 1
x = 1/3
this is correct value of x
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MODELING REAL LIFE A cell phone plan costs $30 for each line.
a. Does the situation represent a function? If so, identify the independent and dependent variables.
the situation represent a function. The total cost of the cell phone plan is the
The domain is
b. You can have a maximum of four lines on a plan. Find the domain and range.
Yes :: No
The range is
:: independent variable :: dependent variable
and the number of cell phone lines is the
a. Yes, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.
What is Domain?
The set of all inputs of the function is called Domain of set.
Given that;
A cell phone plan costs $30 for each line.
Now, Let the number of lines be x and total cost be y.
So, We can evaluate;
y = 30x
Thus, This equation represent Linear function.
So, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
Since, You can have a maximum of four lines on a plan.
So, The possible values are;
x = 0, 1, 2, 3, 4
After substitute all the value of x in equation y = 30x we get;
For x = 0
y = 30 × 0 = 0
For x = 1
y = 30 × 1 = 30
For x = 2
y = 30 × 2 = 60
For x = 3
y = 30 × 3 = 90
For x = 4
y = 30 × 4 = 120
Thus, The range of the function will be 0 ≤ x ≤ 4.
And, The domain of the function will be 0 ≤ y ≤ 120.
Therefore,
a. Yes, The situation represents a function.
The independent variable is number of lines and dependent variable is the total cost.
b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.
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Identify the domain and range of y = [x] + 2.
DOMAIN X CAN BE ALL REAL NUMBERS.
NO MATTER THE VALUE OF X YOU INSERT IT WILL ALWAYS TURN POSITIVE PLUS A POSTIVE TWO. MEANING THERE IS NO WAY THAT YOUR Y CAN BE EQUAL TO 0 OR A NEGATIVE NUMBER THE FUNCTION IS ALWAYSINCREASING FOR ANY VALUE OF Y.RANGE: Y IS ALL THE REAL NUMBERS GREATER THAN 0.
For x = -5, what is the value of 4x²-11x ?
Answer:
155
Step-by-step explanation:
4(-5)^2-11x
-5 squared is 25, times 4 =100, -11times-5 is 55 (positive) so 100+55=155
Find the volume of the figure. Round to the nearest hundredth of a unit.
Check the picture below.
so is more or less the figure of a rectangular prism with a right-cylinder underneath that has a radius of 1, since it has a diameter of 2.
now, if we just get the volume of the prism, and then the volume of half of the cylinder, because only half-cylinder is really inside the prism, and then subtract that half-cylinder volume from that of the prism, what's leftover is the volume of the figure only.
[tex]\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}\hspace{5em}\stackrel{\textit{volume of half a cylinder}}{V=\cfrac{1}{2}\pi r^2 h} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE volumes}}{\stackrel{prism}{(4)(4)(8)}~~ - ~~\stackrel{half~cylinder}{\cfrac{1}{2}\pi (\underset{r}{1})^2(\underset{h}{8})}}\implies 128~~ - ~~4\pi ~~ \approx ~~\text{\LARGE 115.43}~cm^3[/tex]
An astronaut on the moon throws a baseball upward. The height of the ball in feet
(y) is related to the number of seconds since the ball was thrown (x).
y = -2.7x² + 30x + 6.5
How high will the ball be after 3 seconds? Use your calculator to pull up a function
table to help you. (6 points total)
The height of the ball be after 3 seconds will be 72.2 feet.
How to calculate the height?From the information given, it should be noted that the astronaut on the moon throws a baseball upward and the height of the ball in feet
(y) is related to the number of seconds since the ball was thrown (x).
In this case, it should be noted that the function is illustrated as:
y = -2.7x² + 30x + 6.5
Therefore, it was given that x = 3. It should be noted that this will be put back into the function. This will be:
y = -2.7x² + 30x + 6.5
y = -2.7(3)² + 30(3) + 6.5
y = -24.3 + 90 + 6.5
y = 72.2
The height is 72.2 feet.
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Please help me to do this problem please.
In order to find the solution of this compound inequation, let's first divide it in two inequations:
[tex]\begin{cases}-2\le3x+4 \\ 3x+4<13\end{cases}[/tex]Solving the first inequation, we have:
[tex]\begin{gathered} -2\le3x+4_{} \\ -2-4\le3x \\ -6\le3x \\ -2\le x \end{gathered}[/tex]Now, for the second inequation, we have:
[tex]\begin{gathered} 3x+4<13 \\ 3x<13-4 \\ 3x<9 \\ x<3 \end{gathered}[/tex]Putting both solutions together:
[tex]-2\le x<3[/tex]So the correct option is C.
P, R and S are points on a circle
centre O. If PÔR = 150°, calculate PSR
The measure of angle PSR is 105°.
What does the Angle Subtended by an Arc of a Circle Theorem state?An arc's angle at the center of the circle is twice as large as its angle at any other point on the circumference.
Given:
The centre of the circle is O.
P, R, and S are points on a circle.
∠POR = 150°
Let Q be a point on the circumference of the circle with centre O.
By half angle property,
∠POR = 2∠PQR
∠PQR = [tex]\frac{1}{2} * 150[/tex] = 75°
In the figure, the points on the circle PQRS form a cyclic quadrilateral.
A cyclic quadrilateral has opposite angles that measure a total of 180 degrees.
∠PQR + ∠PSR = 180°
∠PSR = 180° - 75°
∠PSR = 105°
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What is the linear equation of (1, -7); slope = -1
The linear equation of given point (1, -7) and slope -1 is y = -x - 6.
What is the point-slope form of linear equations?One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form. The general form of a linear equation is y - y₁ = m(x - x₁) where m is the slope and (x₁, y₁) is the point.It draws attention to the line's slope and one of the line's points (that is not the y-intercept).Given:
Point(x₁ , y₁) = (1, -7)
Slope = -1
By using the Point-slope form of the linear equations, we get
y - y₁ = m(x - x₁)
⇒ y - (-7) = -1(x - 1)
⇒ y + 7 = -x + 1
⇒ y = -x + 1 - 7
⇒ y = -x - 6
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school children shared oranges as follows .Jonas got 1/3 of the total and the remaining were shared between Mary and Rejoice in the ratio 3:2. if Rejoice got 24 oranges How many did Jonas get
The appropriate choice of ratio will be given by
Jonas got 30 oranges
What is ratio?
Ratio determines the comparision among many quantities with the same unit.
Here,
Let Mary got 3x oranges and Rejoice got 2x oranges
By the Problem,
[tex]2x = 24[/tex]
[tex]x = \frac{24}{2}[/tex]
[tex]x = 12[/tex]
Number of oranges Mary got = [tex]12 \times 3[/tex]
= [tex]36[/tex]
Number of oranges shared between Mary and Rejoice = [tex]24 + 36[/tex]
= [tex]60[/tex]
Fraction of oranges shared between Mary and Rejoice = [tex]1 - \frac{1}{3}[/tex]
= [tex]\frac{3 - 1}{3}[/tex]
= [tex]\frac{2}{3}[/tex]
Total number of oranges = [tex]\frac{60}{\frac{2}{3} }[/tex]
= [tex]60 \times \frac{3}{2}[/tex]
= [tex]90[/tex]
Number of oranges Jonas got = [tex]90 \times \frac{1}{3}[/tex]
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A train starts from rest and accelerates uniformly at 1.5m/s²
until it attains a speed of 30m/s. Find the time taken and the
distance travelled.
Answer:
V= 30m/s u=0 A=1.5, time t=? distance S=?
Step-by-step explanation:
to find time:
A=v-u/t
t=v-u/a
t =30-0/1.5
t = 20 secs
to find distance S
S= UT +½at²
S= 0×20+ 1.5×20²/2
s= 300m
Zoe says that 2³ · 4² can be rewritten as 8⁶. Juana says that it can be rewritten as 8⁵. Danladi says that it cannot be rewritten as either of these expressions. Who is correct? Explain.
Answer:
Danladi is correct
Step-by-step explanation:
Danladi is correct because 2^3×4^2 equals 128
8 to the 6th is 262144 and to the 5th is 32768
f(x)=7x-9, f(a +9),what’s the answer HELPME
Step-by-step explanation:
substitute a+9 in place of x in f(x) f(a+9)= 7(a+9) -9 = 7a+63-9 = 7a+54George finished 1/4 of a level of his computer game in 1/3 of an hour. At this rate, how many levels can he finish in one hour?
Let x be the number of game he can finish in 1 hour
1/4 = 1/3 hour
x = 1 hour
cross-multiply
1/3 x = 1/4
Multiply both-side of the equation by 3
x = 3/4 of his level game
He can finish 3/4 of his level game in an hour
To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars.
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
What is meant by expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
The dollar amount the club would contain if they reached half of their goal T + 50.
The dollar amount the club would contain if every student at the school donated 50 cents to the cause 0,5T.
The dollar amount the club could donate if they earned $50 more than their goal of 0.25n.
The dollar amount the club would still require to expand to achieve its goal after every student at the school donated 50 cents 0.5n.
The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.
The complete question is:
To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars. Match each quantity to an expression, an equation, or an inequality that describes it. A: the dollar amount the club would have if they reached half of their goal 1: B: the dollar amount the club would have if every student at the school donated 50 cents to the cause 2: C: the dollar amount the club could donate if they made $50 more than their goal 3: D: the dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents 4: E: the dollar amount the club would have if half of the students at the school each gave 50 cents 5: Which statement matches with T + 50?
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#SPJ13