The direct variation equation is: b) f = 30x.
The distance 420 newtons will stretch is: d) x = 14.
How to Write a Direct Variation Equation?The direct variation equation can be defined as y = kx, where k is the constant of proportionality, which is k = y/x, while x and y are the variables.
Let y represent the distance the spring is stretched, while x represents the force that is applied to the spring.
If a force (f) of 180 newtons is applied to stretch a distance of the spring (x) to 6 cm, therefore:
Constant of proportionality, k = 180/6
Constant of proportionality, k = 30
To write the direct variation equation, substitute k = 30 into f = kx:
f = 30x.
To find the distance (x) the spring will be stretched when 420 newtons was applied, substitute f = 420 into y = 30x:
420 = 30x
420/30 = 30x/30
14 = x
x = 14
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the school cafeteria orders for cartons of regular milk for every three cartons of chocolate milk a. complete the bar diagram to show the ratio b. the school ordered 120 cartons of regular milk. Divide 120 cartons of regular milk by underscore_because there are__boxes in the top row c.write the value of each box in both rows of the bar diagram d.how many cartons of chocolate milk did the school order?
1) Gathering the data
a) Since each Regular milk has four cartons and chocolate 3. If we multiply by 30 we get 120 for Regular Milk and 90 for Chocolate Milk
Regular Milk 4
Chocolate Milk: 3
Regular Milk: 120
Chocolate Milk: 90
The ratio is 4/3, 4 cartons of regular milk for every 3 cartons of chocolate milk.
b) Divide the 120 cartons by 30 because there are 4 boxes in the top row
c) write the value of each box in both rows of the bar diagram
d) According to the bar graph the School ordered 90 cartons of chocolate milk
Suppose the cost per ton y to build an oil platform of x thousand tons is approximately by:What is the cost per ton for x=300?
The cost per ton of x = 300 is 318.18
To solve this, we need to reaplce x in the function:
[tex]\begin{gathered} \begin{cases}f(x)=\frac{262,500}{x+525} \\ x=300\end{cases} \\ f(300)=\frac{262,500}{300+525}=\frac{262,500}{825} \\ f(300)\approx318.18 \end{gathered}[/tex]And then we get the anser
PLEASE HELP ME I WILL MARK YOU BRANLYEST
Solve the inequality and graph the solution.
−0.8b + 2.3 > 8.7
number line with an open circle plotted at negative eight and arrow pointing right
number line with a closed circle plotted at negative eight and arrow pointing right
number line with an open circle plotted at negative eight and arrow pointing left
number line with a closed circle plotted at negative eight and arrow pointing left
The solution of the inequality:
-8 > b
And the graph can be seen below.
How to solve the inequality?Here we start with the inequality:
-0.8*b + 2.3 > 8.7
To solve this we need to isolate the variable b.
Let's do that in the right side:
-8.7 + 2.3 > 0.8*b
-6.4 > 0.8*b
-6.4/0.8 > b
-8 > b
So b is smaller than -8. then the correct graph is:
"number line with an open circle plotted at negative eight and arrow pointing left"
.
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Which is the domain and range of the parabola with the equation y = 0.5(x²-10x-5)?
The domain of the given function is the set of all real numbers that is represented as x ∈ (-∝,∝ ) and range of the function is [-15,∝).
What is domain and range of a function?The set of values that can be plugged into a function is known as its domain. The range of a function is the collection of all potential values that can result from the dependent variable, or the collection of all possible values after substituting the domain.
Domain of a polynomial function is the set of all real numbers which is given by x ∈ (-∝,∝ ).
Since the given function y = 0.5(x^2 - 10x - 5) is a polynomial function, it's domain is x ∈ (-∝,∝ ).
To obtain the range of the function, plot the graph of the parabola which is shown in the figure.
The vertex of the parabola is at (5,15). Value of y does not go below 15. Therefore the set of all possible values that the function takes is given by [-15,∝).
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On a snow day, Robert created two snowmen in his backyard. Snowman A was built to a height of 33 inches and Snowman B was built to a height of 45 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 6 inches per hour and Snowman B's height decreased by 9 inches per hour. Let AA represent the height of Snowman A tt hours after sunrise and let BB represent the height of Snowman B tt hours after sunrise. Graph each function and determine which Snowman is taller after 3 hours.
What is the slope of the line that contains the points (-3, -4) and (-6, 2)?
The slope of the line that contains the (-3, -4) and (-6, 2) is -2.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variables.
The slope is refer to as rise over run.
Therefore, the slope of the line that contains the points (-3, -4) and (-6, 2) can be found as follows:
slope = y₂ - y₁ / x₂ - x₁
where
x₁ = - 3
x₂ = - 6
y₁ = - 4
y₂ = 2
Therefore,
slope = m = 2 + 4 / -6 + 3
slope = 6/ -3
Therefore,
slope = - 2
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What is the value of x-9 if x = -24?
A. 33
B. 15
C. -15
B. -33
Answer:
D
Step-by-step explanation:
don't forget to follow rate like
Answer:
The second B) - 33
Step-by-step explanation:
-24 - 9 = -33.
Consider a set of data in which the sample mean is 23.8 and the sample standard deviation is 6.6. Calculate the z score given that x= 26.7 round your answer two decimal places.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} mean(\mu)=23.8 \\ standard\text{ }deviation(\sigma)=6.6 \\ x=26.7 \end{gathered}[/tex]STEP 2: Write the formula for calculating z-scores
[tex]z=\frac{x-\mu}{\sigma}[/tex]By substitution,
[tex]\begin{gathered} z=\frac{26.7-23.8}{6.6}=\frac{2.9}{6.6}=0.43939393939 \\ \\ z\approx0.44 \end{gathered}[/tex]Hence, the z score is approximately 0.44 to 2 decimal places
help me please, correct answer gets brainliest
Answer:
Only D and B
Step-by-step explanation:
How to convert 1 million seconds to hours
Solution
Step 1
To convert seconds to hours, divide the seconds by 3600.
Step 2
1 million seconds = 1000000 seconds
[tex]\begin{gathered} To\text{ hours} \\ \\ \text{= }\frac{1000000}{3600} \\ \\ =\text{ }277\frac{7}{9}\text{ hours} \end{gathered}[/tex]Write all integers that belong to the intervals:[-1, 1]
Okay, here we have this:
Considering that the intervals are closed, we have the following integers in this interval: -1,0,1.
Question 7After Anishing his workout,Justin's heart rate decreased 3beats per minute for each of thenext 4 minutes. What was thechange in Justin's heart rateafter 4 minutes?
Justin"s heart rate decreased 3 beats per minute for each of next 4 minutes
Let his heart rate be be 1
For the first minutes
1 minute his heart rate was 1 - 3 = -2
This is because the heart rate is decreasing 3 beats per minutes
2minutes later, his heart beat will be -2 -3
-2 - 3 = -5
3 minutes later, his heart beat will be -5 - 3
-5 - 3 = -8
4 minutes later, -8 - 3
-8 - 3 = -11
Change = Final heart beat - initial heart beat / initial heart beat
Change = -11 -2 / -2
Change = -13/-2
Change = 13/2
= 6.5
Question 1 Which expression is equivalent to r-1.y? a Ob y? Ос ty-2 Od xy2
Step 1
State a law of indices that can be used to simplify the problem
[tex]\begin{gathered} a^{-1\text{ }}=\frac{1}{a^{-1}} \\ \end{gathered}[/tex]Step 2
Apply this to the question and get the solution
[tex]\begin{gathered} x^{-1\text{ }}=\text{ }\frac{1}{x} \\ \text{Hence} \\ \frac{1}{x}.y^2^{} \\ =\frac{y^2}{x} \end{gathered}[/tex]Hence option B
1. How many total engineers liked science 2. Which type of engineer was surveyed the most 3. P(mechanical engineer)4. P(engineer who liked math)5. P(engineer who liked science or is a chemical engineer)6. P(electrical or chemical engineer)7. P(mechanical engineer who liked science)8. P(engineer who liked math and is an electrical engineer)Answer the following problems about two way frequency tables fill in the missing cells of each table make sure to reduce your fraction.
Step 1; Complete the table
1. The number of engineers that like science are 266
2. The engineer surveyed the most is Electrical Engineers
3. Pr(mechanical Engineer) is
[tex]\begin{gathered} \frac{total\text{ number of mechanical engin}er}{\text{total}} \\ \text{Total number pf mechanical engine}er\text{ =170} \\ \text{Total =516} \\ =\frac{170}{516} \\ =0.33 \end{gathered}[/tex]4. Pr(engineer who liked maths ) is
[tex]\frac{Total\text{ number of engin}er\text{ who liked maths }}{ground\text{ total}}=\frac{254}{516}=0.49[/tex]5. Pr( Engineer who like science or is a chemical engineer) is
Let Pr(engineer like science)=E and Pr(a chemical engineer)=S
The Pr( Engineer who like science or is a chemical engineer) is given as
[tex]\begin{gathered} Pr(E)+Pr(S)-Pr(\text{EnS)} \\ \text{where Pr(E)=}\frac{262}{516},\text{ Pr(S)=}\frac{171}{516},\text{ Pr(EnS)=}\frac{91}{516} \end{gathered}[/tex]Hence, we have
[tex]\begin{gathered} \frac{262}{516}+\frac{171}{516}-\frac{91}{516} \\ =\frac{262+171-91}{516}=\frac{342}{516}=0.66 \end{gathered}[/tex]6. Pr( Electrical or chemical) is
[tex]\begin{gathered} Pr(\text{Electrical) +Pr(chemical)} \\ Pr(\text{electrical)}=\frac{175}{516},\text{ Pr(chemical)}=\frac{171}{516} \\ \text{hence,} \\ \frac{175}{516}+\frac{171}{516}=\frac{346}{516}=0.67 \\ \end{gathered}[/tex]7. Pr(Mechanical engineer who liked science) is given as
[tex]\begin{gathered} Pr(M|S)=\frac{Pr(MnS)}{Pr(S)} \\ Pr(MnS)=\frac{81}{516},\text{ Pr(S)=}\frac{262}{516} \\ Pr(M|S)=\frac{81}{516}\times\frac{516}{262}=\frac{81}{262}=0.31 \end{gathered}[/tex]8. Pr(an engineer who liked maths and is an electrical engineer)
[tex]\frac{85}{175}=0.49[/tex]One popular smoothie recipe uses 2/3 oz of acai juice to make one smoothie. Acai juice typically comes in a 5-oz container, and you want to know how many smoothies can be made from one container. (Write both a multiplication equation and division equation that represents this scenario) (Determine the number of smoothies can be made from one oz of acai)
You can make one and a half smoothies from one oz of acai juice
How to write multiplication equation and division equation?
Given that:
smoothie recipe uses 2/3 oz of acai juice to make one smoothie and
Acai juice comes in a 5-oz container
In order to know how many smoothies can be made from one container, you divide the volume of the Acai juice container by the volume needed to make one smoothie. Thus the equation is:
No. of smoothies = volume of container/volume needed for one smoothie
The number of smoothies that can be made from one oz of acai is:
No. of smoothie = 1/(2/3) = 1 1/2 smoothies
Therefore, the number that can be made from one oz is one and half smoothies
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How to find the products of binomials
Answer:
FOIL Method! (EXPLAINED BELOW)
Step-by-step explanation:
FOIL MEANS First Out In Last.
For example:
Binomial: (a+b) (a+b)
STEP 1: Multiply the first term of each bracket.
(a+b) (a+b)
So, a * a = [tex]a^{2}[/tex]
The number would be positive since both terms are positive.
STEP 2: Multiply the outer terms.
(a+b) (a+b)
So, a * b = ab
The number would be positive since both terms are positive.
STEP 3: Multiply the inner terms.
(a+b) (a+b)
So, a * b = ab
The number would be positive since both terms are positive.
STEP 4: Multiply the last terms.
(a+b) (a+b)
So, b * b = [tex]b^{2}[/tex]
The number would be positive since both terms are positive.
STEP 5: Put them together with the appropriate signs.
[tex]a^{2} + 2ab + b^{2}[/tex]Which describes how to find all rotation angles less that 360° that will map a regular polygon onto itself?
This question is about rotations of polygons.
To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.
To know the exact angle rotation to map the polygon onto itself, we just have to divide 360° by the number of sides.
Therefore, the right answer is the third choice.Answer:
This question is about rotations of polygons.
To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.
To know the exact angle rotation to map the polygon onto itself, we have to divide 360° by the number of sides.
Therefore, the right answer is the third choice.
Step-by-step explanation:
Jayson reads the first 48 pages of a 480-page book in 3 days. marcus reads the first 50 pages of a 400-page book in 4 days. nina reads the first 120 pages of a 600-page book in 5 days. check your work on zearn. 1. if they continue to read at these rates, who will finish first? will finish the book first. 2. how many days will each student take to finish his or her book? it will take jayson days to finish his book. it will take marcus days to finish his book. it will take nina days to finish her book.
Nina will take the shortest time finishing her book.
What is division ?Division is the opposite of multiplication. If you divide 12 into three equally sized groups, you will get four in each group if the three groups of four sum up to 12, which they do when you multiply. The main goal of division is to count the total number of evenly distributed groups or the total number of people in each group following a fair distribution.
CalculationLet's calculate how many pages each person reads in one day:
Jayson ⇒ 48 pages / 3 days = 16 pages/dayMarcus ⇒ 50 pages / 4 days = 12.5 pages/dayNina ⇒ 120 pages / 5 days = 24 pages/dayThen we divide the number of pages of each book by reading speed of the respective person:
Jayson ⇒ 480 pages ÷ 16 pages/day = 30 daysMarcus ⇒ 400 pages ÷ 12.5 pages/day = 32 daysNina ⇒ 600 pages ÷ 24 pages/day = 25 daysThus Nina will take the shortest time finishing her book.
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Graph the function h(x)=. I have a picture of the problem
Let's begin by listing out the given information
[tex]\begin{gathered} h(x)=-\frac{2}{3}x-2 \\ h(x)=y \\ y=-\frac{2}{3}x-2 \end{gathered}[/tex]We will graph the function by assuming values for the independent variable (x = -3, 0, 3
[tex]\begin{gathered} y=-\frac{2}{3}x-2 \\ x=-3 \\ y=-\frac{2}{3}(-3)-2=2-2=0 \\ (x,y)=(-3,0) \\ x=0 \\ y=-\frac{2}{3}(0)-2=0-2=-2 \\ (x,y)=(0,-2) \\ x=3 \\ y=-\frac{2}{3}(3)-2=-2-2=-4 \\ (x,y)=(3,-4) \end{gathered}[/tex]We will plot the ordered points (shown below)
Connor filled his 108 gallon pool with water in 8 hours. How many gallons per
hour did he use?
Answer:
I'm pretty sure it's 13.5.
Step-by-step explanation:
Boom first let's do 108 ÷ 8
After that you should get 13.5.
13 and a half gallons per hour.
Given the inequality 4(n-5) <3(n + 11), determine which integer makes the inequality false.
S:{4}
S:{11}
S:{53}
S:{-8}
The integer n = 53 will make the inequality 4(n - 5) < 3(n + 11) false
InequalityIn mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
In this expression, we can solve and find what makes it's true and take the odd one out.
4(n - 5) < 3(n + 11)
4n - 20 < 3n + 33
n < 53
From the options given, the value of n that will make the inequality true is less than 53 and that makes the integer 53 to be false.
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What is the measure of n?
5
15
m
n= [?l
The measure of the hypotenuse n is 5√3
Hypotenuse
Hypotenuse refers the longest side of a right-angled triangle, the side opposite the right angle. And the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
Given,
Here we have the triangle with some measures on it.
Here we need to find the value of n.
While we looking into the diagram, we have identified that, n is the hypotenuse of the triangle,
So, the value of n is the root of the product of the two hypotenuse segments it touches:
=> n = √(5·15)
=> n = √75
It can be simplified as,
=> n = √(3 x 25)
=> n = 5√3
Therefore, the value of n is 5√3.
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Question 3(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In AJKL, mZJ = 67° and mL = 90°. Determine the measure of the exterior angle to ZK.
23°
113°
O 157°
O 78.5°
By applying the exterior angle theorem, the measure of the exterior angle to angle ZK in triangle JKL is equal to 157°
What is the exterior angle theorem?In Mathematics, the exterior angle theorem can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
How to determine the value of angle ZK?In order to determine the value of ∠G in triangle JKL (ΔJKL), we would have to apply exterior angle theorem. Mathematically, the exterior angle theorem can be used to model the angles in triangle JKL (ΔJKL) and this is given by:
m<G = m<ZJ + m<L
Substituting the given parameters into the formula above, we have;
m<ZK = 67° + 90°.
m<ZK = 157°.
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factor out the coefficient of the variable term 4x-20
the given expression is,
4x - 20 = 0
here 4 is the coefficient of variable x
4x = 20
x = 20/4
x = 5
thus, the value of x is 5
What is an equation of the line that passes through the point (2,-5)(2,−5) and is parallel to the line x-2y=16x−2y=16?
The slope intercept form of the required line is x -2y = 12
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The given line is
[tex]x - 2y = 16\\2y = x - 16\\y = \frac{1}{2}x - \frac{16}{2}\\[/tex]
Slope of the line = [tex]\frac{1}{2}[/tex]
Slope of the line parallel to this line = [tex]\frac{1}{2}[/tex]
The line passes through (2, -5).
Equation of the required line-
[tex]y - (-5)= \frac{1}{2}(x - 2)\\2y + 10 = x - 2\\ x - 2y = 10 + 2\\x-2y = 12[/tex]
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The track team has 11 distance runners but can only enter five in the meet. How many combinations of five runners can the coach create?.
Answer:
55
Step-by-step explanation:
11 x 5 = total combinations
11 x 5 = 55
Identify the maximum or minimum point from the graph:f(x)=|x-3|Answer as an ordered pair (x,y)
we have
f(x)=|x-3|
the vertex of the function is the point (3,0)
the function has a minimum
the vertex is the minimum
so the answer is
the minimum is the point (3,0)Cuatro pintores tardan 6,3 horas en pintar un almacén. Se decide contratar a 9 pintores.
a) ¿Cuánto tardarán en pintar el almacén? Expresa el resultado en formato de horas y minutos. (Como por ejemplo: 3 horas 15 minutos.)
b) ¿Cuánto hay que pagar en total por el trabajo a los nueve pintores si cada pintor cobra 8,5 euros por hora trabajada?
By using unitary method, it is obtained that
a) 9 painters took 2hours 48 minutes to paint a ware house
b) 9 painters earns 214.2 euros by working 2.8 hours
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, unitary method is used
a) Four painters took 6.3 hours to paint a ware house
1 painter take [tex]6.3 \times 4[/tex] hours to paint a ware house
9 painters took [tex]\frac{6.3 \times 4}{9}[/tex] hours to paint a ware house
9 painters took 2.8 hours to paint a ware house
9 painters took 2hour + [tex]0.8 \times 60[/tex] minutes to paint a ware house
9 painters took 2hours 48 minutes to paint a ware house
b) Each painter earns 8.5 euros per hour worked
Each painter earns 8.5 [tex]\times[/tex] 2.8 euros by working 2.8 hours
9 painters earns 8.5 [tex]\times[/tex] 2.8 [tex]\times[/tex] 9 euros by working 2.8 hours
9 painters earns 214.2 euros by working 2.8 hours
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If Miss. lora has 4 people in her class and she has 28 more. How many people are in her class.
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
sorry no Step-by-step explanation
Carlos had 194 seeds and 11 flower pots. He put the same number of seeds in each flower pot. Which is the best estimate for the number of seeds in each flower pot?
a:10
b:20
c:30
d:40
Answer: B
Step-by-step explanation: The question says estimate, meaning you'll have to round the numbers. 194 gets rounded up to 200, while 11 gets rounded down to 10.
200 / 10 = 20, thus the answer is B