7/20 can't be reduced to 3/5
One-sixth of the fourth graders and one-third of the fifth graders miss school on Friday. The absentee sheet for Friday shows the names of 9 fourth graders and 16 fifth graders. How many fourth and fifth graders are enrolled in the school?
Answer:
There are 54 4th graders.
There are 48 5th graders.
Step-by-step explanation:
1/6 of the 4th graders is 9 students.
1/6 x = 9
x = 9 × 6
x = 54
There are 54 4th graders.
1/3 of the 5th graders is 16 students.
1/3 x = 16
x = 3 × 16
x = 48
There are 48 5th graders.
There are 54 Fourth grader and 48 Fifth graders were enrolled in the school.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number of fourth graders be x.
and, let the number of fifth graders be y.
As, One-sixth of the fourth graders is 9.
and, one-third of the fifth graders is 16.
Then, 1/6 x = 9
x= 54
and, 1/3 y= 16
y= 48
Hence, there are 54 Fourth grader and 48 Fifth graders were enrolled in the school.
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Write an expression to represent:The sum of one and the product of one and a number I.Stuck? Watch a video or use a hint.Written in expression to represent the sum of one and a product of one and a number x
In this case, we'll have to carry out several steps to find the solution.
Step 01:
We must analyze the problem to write the expression.
Step 02:
The expression is:
x = number
1 + 1 * x
The solution is:
1 + 1 * x
Need help with this question please!
Answer: the picture
Step-by-step explanation:
Ty hiked up a mountain to 2523 meters above sea level. Pete is a scuba diver and dove 319 meters below sea level. If Ty and Pete started at the same elevation, how much higher was Ty than Pete when they were the farthest apart?
Ty hiked up a mountain to 2523 meters above sea level.
Height of the TY above the sea level = 2523meter
. Pete is a scuba diver and dove 319 meters below sea level
Depth of the Pete = 319 meter
To find the how much higher was Ty than Pete,
Find the differecne between thier disatnce from sea level
[tex]\begin{gathered} Ty\text{ was higher than Pete=2523-319} \\ Ty\text{ was higher than pete by }2204\text{ meter} \end{gathered}[/tex]Answer: Ty was 2204 meter higher than Pete
Show fraction 15/4 on a number line
Given data:
The given number is a=15/4.
The given number can be written as,
[tex]\begin{gathered} a=\frac{15}{4} \\ =3.75 \end{gathered}[/tex]The numberr can be expression on the number line between 3 and 4 but it is more close to 4.
Three Turtles are racing . Abe the turtle's distance is represented by the green line, Benji the turtle's distance is represented by the red line, and Carter the turtle's distance is represented by the bule line. Use the graph to answer the following questions.
Using the graph we can see that Benji (the red line) goes 50 feet far, also by looking at the graph we see tht Carter (the blue line) takes 240 seconds to travel 80 feet.
If they are racing I would pick the one who takes less time to travel more distance, by the graph we see that Carter is faster than Benji and Abe.
can you please solve this practice problem for me I need assistance C. -1/2 and D. 1/2
We are going to select the points when x = 0 and x = 2.
Observing the graph we see that when x = 0, then y = 1 - (0,1)
when x = 2, then y = 2 - (2, 2)
Now we have two points:
(x₁, y₁) = (0, 1)
(x₂, y₂) = (2, 2)
Step 2: change of variablesWe are going to find how much the variables change from point 1 to point 2
Change of x:
Δx = x₂ - x₁ = 2 - 0 = 2
Δx = 2
Change of y:
Δy = y₂ - y₁ = 2 - 1 = 1
Δy = 1
Step 3: slopeThe slope, m, is the division of the two found changes:
m = Δy/Δx = 1/2
Answer: D. 1/2xy12364468710 a. Construct a scatterplot. b. Is there a linear association, nonlinear association, or no association? c. Compute r. d. On the basis of the scatterplot and r, determine the strength of the association? Explain.
SOLUTION:
(a) From the given table, we are to construct a scatterplot.
(b) There is a strong linear association because all the points align themselves in a near perfect straight line.
(c) To Compute r;
(d) We are to determine the strength of the association;
Because r = 0.9934 which is very close to 1.0, so we conclude that the strength of the association is very strong.
Set up and solve a proportion for the following application problem. If 6 pounds of grass seed cover 366 square feet, how many pounds are neededfor 4392 square feet?am 24/7onlinepounds
We know that 6 pounds cover 366 square feet, then we have the ratio:
[tex]\frac{6}{366}[/tex]Let x be the amount we need to cover 4392 square feet, then we have the ratio:
[tex]\frac{x}{4392}[/tex]Since the ratios have to be equal we have the proportion:
[tex]\frac{x}{4392}=\frac{6}{366}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{x}{4392}=\frac{6}{366} \\ x=4392\cdot\frac{6}{366} \\ x=72 \end{gathered}[/tex]Therefore, 72 pounds are nedded for 4392 sq ft.
How many significant figures will there be in answer to the following problem?6.783 - 2.56 =
We need to make the substraction:
[tex]6.783-2.56[/tex]We do that as follows:
The number of significant figures in how many numbers we have in the answer, in this case the answer has 4 numbers, thus it has 4 significant figures.
Which describes a bar diagram showing the percent of students who participated in dances?1 shaded square out of 10 squares2 shaded squares out of 10 squares3 shaded squares out of 10 squares4 shaded squares out of 10 squares
From the information on the pie chart, the proportion of students that participated in dances is 20 out of 100.
Then, if we represent this in a bar chart where 100% is 10 squares, the proportion of students that participated in dances should be represented by:
[tex]\begin{gathered} 100\%\longrightarrow10\text{ squares} \\ \frac{20}{100}\cdot100\%=20\%\longrightarrow\frac{20\%}{100\%}\cdot10=2\text{ squares} \end{gathered}[/tex]Answer: 2 shaded squares out of 10 squares
Maria invested her savings in two investment funds. The amount she invested in Fund A was $7000 less than the amount she invested in Fund B. Fund Areturned a 7% profit and Fund B returned a 3% profit. How much did she invest in Fund B, if the total profit from the two funds together was $1610?
It is given that,
The amount she invested in Fund A was $7000 less than the amount she invested in Fund B.
So, A=B-7000
And it is given that, Fund A returned a 7% profit and Fund B returned a 3% profit.
The total profit from the two funds together was $1610.
It can be written as,
7% of A +3% of B=1610
Substitute A=B-7000, we get
7% of (B-7000) +3% of B=1610
On solving we get,
[tex]\begin{gathered} \frac{7}{100}(B-7000)+\frac{3}{100}B=1610 \\ \frac{7}{100}B-490+\frac{3}{100}B=1610 \\ \frac{10}{100}B-490=1610 \\ \frac{1}{10}B=1610+490 \\ \frac{1}{10}B=2100 \\ B=21000 \end{gathered}[/tex]Hence, the investment in fund B is $21,000.
Sam and Sophia participates in a dice game. Sophia rolls one die. She gets $2 if 5 turns up. She gets $3 if 6 turns up. She loses $10 if 2 turns up. She neither wins nor loses if any other face turns up. Is this game fair?The game is not fair and not favorable to player.The game is not fair, but favorable to player.The game is fair.The game is fair, but not favorable to player.
Hello there. To solve this question, we need to analyze the probabilities for each case and see if the game is fair or not and also favorable to the player.
Sophia rolls a dice. If 5 turns up, she gets $2; If 6 turns up, she gets $3; If 2 turns up, she loses $10; She neither wins nor loses if any other face turns up.
First, let's remember something that will be important: a dice only haves 6 faces.
As we can see, she is winning (getting money) if 2 out of 6 faces turns up (5 and 6), and is losing if 1 out of 6 faces turns up (2). She is neither winning or losing if 3 out of 6 faces turns up (1, 3, 4).
About the fairness of the game, there are only 1 case she loses and 2 cases she wins something. We could only say the game is fair if the amount of winning cases were equal to the amount of losing cases. The game is not fair.
About being favorable, we'll consider it being unfavorable just the case that she loses money. The first and third cases, in which she gets money or doesn't get or lose money are favorable to her.
Since only 1 out of 6 faces makes her lose, then the game is favorable to the player.
Final answer: The game is not fair, but favorable to the player.
A ball is dropped from a height of 18 feet.The function f(x) = 18(0.75)* gives theheight in feet of each bounce, where x isthe bounce number. What will be theheight of the third bounce to the nearesttenth of a foot?
The height of the third bounce to the nearest tenth of a foot is 7.6 ft
Explanation:The given function:
[tex]f(x)\text{ = }18\mleft(0.75\mright)^x[/tex]f(x) = height in feet of each bounce
x represent the bounce number
For the third bounce, x = 3
replacing x with 3:
[tex]\begin{gathered} f(x)=18(0.75)^3 \\ f(x)\text{ = 18(0.4219)} \end{gathered}[/tex][tex]\begin{gathered} f(x)\text{ = }7.5942 \\ To\text{ the nearest tenth of foot = 7.6 ft} \end{gathered}[/tex]The height of the third bounce to the nearest tenth of a foot is 7.6 ft
01018Annual SalaryANNUAL SALARY VERSUSYEARS OF SERVICE$60,000$50,000$40,000$30,000$20,0005 10 15 20Years of ServiceIn the scatterplot above, each dot represents the annual salary and corresponding years of service for each ofthe 19 employees at Company X. How many of the employees have more than 10 years of service but anannual salary of less than $40,000 ?
To determine how many employees have more than 10 years of service we need to look for dots that are to the right of the "10" position on the horizontal axis. There are a total of 11 employees that fit that criterion. We now need to look for which of these 11 employees earn less than 40,000 per year, for that we have to find the number of dots below the line of 40,000 and to the right of 10 years of service. There are a total of 5 dots.
There are 5 employees with more than 10 years of service which earn less than $40,000.
Points that lie on the same line are called:A. non-collinear and non-coplanarB. opposite raysC. coplanar and non-collinearD. collinear and coplanar
When two points lie on the same line are called collinear. When they lie on the same plane they are called coplanar.
Points that lie on the same plane are not necessarily collinear.
When points are collinear, they lie on the same plane. Then when points are collinear they are necessarily coplanar. But when they are coplanar they are not necessarily colinear.
This means that points that lie on the same line are collinear and coplanar too.
ANSWER: Dhelpppppppppppppppppppp
Ben needs to graph the function f(x)=3(0.1)x. He creates a table of values, using integer values for x.
What does Ben's graph look like?
Drag a value or word to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
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Ben's graph passes through the ordered pairs (−1,Response area), (0, Response area), and (2,Response area). The graph Response area left to right.
Answer:
is there a pitcher that comes with it ?
Step-by-step explanation:
Find the equation in slope-intercept form of the line passing through the points with the given coordinates.(5,2), (5,6)
Given,
The line is passing through the points (5,2), (5,6).
The standard equation of line passing through two points is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substituting the values of coordinates then,
[tex]\begin{gathered} y-2_{}=\frac{6_{}-2_{}}{5_{}-5_{}}(x-5) \\ y-2=\frac{4_{}}{0_{}} \\ y-2=\infty\mleft(x-5\mright) \\ \frac{y-2}{\infty}=x-5 \\ 0=x-5 \\ x=5 \end{gathered}[/tex]Hence, the equation of line passing through point (5,2) and (5,6) is x=5.
Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Why can she now conclude that diagonal W
Mai can conclude that "XWYZ will be the rhombus when we connect WYZ and WYX as all the sides are equal. In a rhombus, the opposing sides are parallel. In a rhombus, the opposing angles are equal. Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals."
What is rhombus?A quadrilateral with equal-length sides is a rhombus. The angles at the opposite vertex are equal, and the opposite sides are parallel. In a rhombus, the opposing sides are parallel. In a rhombus, the opposing angles are equal. Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals.
What is diagonal?A diagonal in mathematics is a line that joins two solids or polygons whose vertices are not on the same edge. Generally speaking, a diagonal is a sloping or slanting line that joins the vertices of a shape. The term "diagonal" refers to lateral shapes with sides, edges, and corners. A diagonal is a line segment that joins two opposing polygonal vertices (or corners). In other words, a diagonal is a line segment that joins two polygonal vertices that are not adjacent to one another. It connects a polygon's vertices, excluding the figure's edges.
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a tunnel is in the shape of a parabola. The maximum height is 48 and it is 18 m wide at the base. What is the vertical clearance 3 m from the edge of the tunnel?
The vertical clearance 3 m from the edge of the tunnel at 19.1 m.
What is referred as the parabola?A parabola is just a U-shaped plane curve in which any point is an equal distance from both a fixed point (recognized as the focus) and a fixed straight line (known as the directrix).For the parabola's maximum height is 50 m, its formula is of the form.
y = ax² + 48
The vertex is located at in this equation (0,48).
Is for vertex to be the maximum of y, the constant a must be negative.
The parabola's base is 18 m wide.
As a result, the x-intercepts seem to be (9,0) and (-9,0).
Set x = 9 and y=0 to obtain
a(9²) + 48 = 0
81a = -48
a = -0.59
The equation of the parabola is
y = - 0.59x² + 48
At 21.32 m of the edge of the tunnel, x = 9 - 2 = 7 m.
Thus, the height of the tunnel (vertical clearance) at x = 7 m is
h = y(7)
= -0.59(7²) + 48
h = 19.09
h = 19.1 m
Thus, the vertical clearance 3 m from the edge of the tunnel at 19.1 m.
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Solve the equation. 1 / 3X - 9 = -12
x=-9
Explanation
[tex]\frac{1}{3}x-9=-12[/tex]
Step 1
add 9 in both sides
[tex]\begin{gathered} \frac{1}{3}x-9=-12 \\ \frac{1}{3}x-9+9=-12+9 \\ \frac{1}{3}x=-3 \end{gathered}[/tex]Step 2
multiply both sides by 3
[tex]\begin{gathered} \frac{1}{3}x=-3 \\ \frac{1}{3}x\cdot3=-3\cdot3 \\ x=-9 \end{gathered}[/tex]I hope this helps you
Answer:
x=-9
Step-by-step explanation:
Solve for X by simplifying both sides of the equation, then isolating the variable. So, pretty much the other dude is right.
- Consider the function represented by this table of values.Xу6385324263 202 14Which function could have produced the values in the table?Ay = 6x + 2By = -6x + 2C) y = (x - 116y = -x - 44
Upload the picture please,
First you need to find the slope using the formula
Slope = (y2 - y1) / (x2 - x1)
Choose two points from the table
P1 = (6, 38)
P2 = (5, 32)
Identify x1, y1, x2, y2
x1 = 6 y1 = 38 x2 = 5 y2 = 32
Substitute the values to find the slope
slope = m = (32 - 38) / (5 - 6)
= -6/-1
= 6
Find the equation of the line using the formula
y - y1 = m(x - x1)
x1 = 6 y1 = 38
Substitution
y - 38 = 6(x - 6)
Simplify
y - 38 = 6x - 36
Solve for y
y = 6x - 36 + 38
y = 6x + 2
how much popcorn would each person get if two shared a half a bag of popcorn equally
Half bag = 1/2 bag
Number of persons = 2
Then divide
(1/2 bag)÷2 = 1/4 bag
Each person will have 1/4 of a bag
I need help seeing how this works out because what I am doing is not right
We will have the following:
AB and CD related in terms of x and y will be:
[tex]\begin{gathered} AB=CD\Rightarrow x+y=2x-y-2 \\ \\ \Rightarrow2y=x-2\Rightarrow y=\frac{x}{2}-1 \end{gathered}[/tex]So, the equation that relates AB and CD is:
[tex]y=\frac{x}{2}-1[/tex]BC and DA in terms of x and y is:
[tex]\begin{gathered} BC=DA\Rightarrow x+2y=3x-3y+2 \\ \\ \Rightarrow5y=2x+2\Rightarrow y=\frac{2}{5}x+\frac{2}{5} \end{gathered}[/tex]So, the equation that relates BC and DA is:
[tex]y=\frac{2}{5}x+\frac{2}{5}[/tex]Now; we determine the values of x & y as follows:
[tex]\begin{gathered} \frac{x}{2}-1=\frac{2}{5}x+\frac{2}{5}\Rightarrow\frac{1}{10}x=\frac{7}{5} \\ \\ \Rightarrow x=14 \end{gathered}[/tex]Then:
[tex]y=\frac{(14)}{2}-1\Rightarrow y=6[/tex]So, the values are:
[tex]\begin{gathered} x=14 \\ \\ y=6 \end{gathered}[/tex]5x + 12 - 9x - 4 - 16
This problem is about a simple algebraic expression which we need to reduce in its simplest form. To do that, we need to reduce like terms, that is, terms that are similar, for example, terms 5x and 9x are similar because they have the same variable; also terms 12, 4, and 16 are also similar because they are single numbers.
Now, we reduce them using the algebraic sum properties, that is, numbers with the same sign will sum, and numbers with different signs will subtract:-
[tex]5x+12-9x-4-16[/tex]Then, we have
[tex]-4x-8[/tex]Therefore, the simplest expression is -4x-8.If the x intercept of a line is positive and the y intercept is negative does the line slant upward or downward?
ANSWER:
slant upward
STEP-BY-STEP EXPLANATION:
The line would slant upward to the right because if the y-intercept is negative, the line starts below the x-axis and if the x-intercept is positive, it means the line continues from below the x-axis and crosses to the right. right. from the origin (to the right of 0), which means that it is tilted up to the right.
We can rectify it in the following graph
If g(x) = 2x-10 what is g(7)?
Answer:
4
Explanation:
Given the below function;
[tex]g(x)=2x-10[/tex]To find g(7), all we need to do is substitute the x for 7 in the below and solve;
[tex]g(7)=2(7)-10=14-10=4[/tex]Help solving these problems
Therefore, when daily output is 106300 units, the cost will be at its lowest.
Define costs.The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function. The average cost function is defined as A(x)=C(x)x, where x > 0. The average cost per unit is calculated by dividing the total cost by the number of units produced. Costing is necessary to make sure that all costs are met and that the group decides on a price that will result in a profit. Finding ALL of a company's costs, including manufacturing, sales, administration, overhead, etc., is the first and most crucial stage. Costs are then divided into fixed and variable costs.
Given,
C=0.04x2 - 8.504x + 25302....... (1), where x is the number of units produced in thousands, gives the cost of generating x thousands of units of lemon-scented widgets in a day.
We must determine the daily production rate that will reduce costs.
dC/dx = 0
The current prerequisite for minimum cost is
0.08x - 8.504 = 0
0.08x = 8.504
x = 106.3
In light of equation (1),
x =106.3
Therefore, when daily output is 106300 units, the cost will be at its lowest.
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The question: A box is a right rectangular prism with the dimensions 8 inches by 8 inches by 14 inches. What is the surface area of this box?
Given the length (l), the width (w), and the height (h) of the rectangular prism:
[tex]\begin{gathered} l=8in \\ w=8in \\ h=14in \end{gathered}[/tex]You need to use this formula for calculating the surface area of a rectangular prism, in order to find the surface area of the box:
[tex]SA=2wl+2hl+2hw[/tex]Where "l" is the length, "w" is the width, and "h" is the height of the rectangular prism.
Therefore, when you substitute the values into the formula and evaluate, you get:
[tex]\begin{gathered} SA=(2)(8in)(8in)+(2)(14in)(8in)+(2)(14in)(8in) \\ \\ SA=128in^2+224in^2+224in^2 \end{gathered}[/tex][tex]SA=576in^2[/tex]Hence, the answer is:
[tex]SA=576in^2[/tex]Answer:c 565
Step-by-step explanation:
as shown above a classic deck of card is made up of 52 cards suppose one card is selected at random and calculate the following probability
Given a classic deck of cards made up of 52 cards
Made up of 13 spades, hearts, diamonds and clubs each,
The formula of Probabaility is given below as,
[tex]\text{Probabilty}=\frac{\operatorname{Re}quired\text{ outcome}}{Possible\text{ outcome}}[/tex]Where the Possible outcome = 52
The probability that a 6 of diamonds is selected is,
[tex]\begin{gathered} \text{required outcome = 1} \\ \text{Probability of a 6 of diamonds=}\frac{1}{52} \end{gathered}[/tex]Probability that a 6 of diamonds is selected is 1/52
The probability that a heart or a diamond is selected,
[tex]\begin{gathered} Probabilty\text{ of a heart P}(H)\text{=}\frac{13}{52} \\ \text{Probability of a diamond=}\frac{13}{52} \\ \text{Probability of a heart or a diamond=}\frac{13}{52}+\frac{13}{52}=\frac{1}{4}+\frac{1}{4}=\frac{1}{2} \end{gathered}[/tex]Probability that a heart or a diamond is selected is 1/2
Probability that a number smaller than 4 (counting the ace as 1) is selected is,
[tex]\begin{gathered} \text{Probability of picking a ace=}\frac{4}{52} \\ \text{Probability of picking a 2=}\frac{4}{52} \\ \text{Probability of picking a 3=}\frac{4}{52} \\ \text{Probability of picking a number smaller than 4=}\frac{4}{52}+\frac{4}{52}+\frac{4}{52}=\frac{3}{13} \end{gathered}[/tex]Probability that a number smaller than 4 (counting the ace as 1) is selected is 3/13