SOLUTION
We know that the cooking club made pies to sell, but we don't know how many pies the cooking club made. So, let the number of pies the cooking club made be x.
Now the cafeteria contributed 4 pies that were cut into 5 pieces and sold. So the cafeteria contributed
[tex]4\text{ pies }\times5\text{ pieces = 20 pieces }[/tex]The cafeteria contributed 20 pieces.
Also we were told that a total of 60 pieces were sold. So what the club sold should be 60 pieces in total minus what the cafeteria sold.
So we have
[tex]60-20=40\text{ pieces }[/tex]The club sold 40 pieces.
Now remember that a pie is cut into 5 pieces, so this means that 40 pieces should make
[tex]\frac{40}{5}=8\text{ pies}[/tex]Hence the club made 8 pies
a pilot took 1/2 hour to complete 1/3 of hjis trip. How much longer will it take him to complete his trip
It took the pilot half an hour to complete one-third of the trip, to determine how much it will take him to complete the trip, you can use cross multiplication to determine it.
1/3 of the trip → 1/2 hour
Whole trip → x hours
Let "1" represent the whole trip, that is, all three parts of it. Both relationships are at the same ratio so that:
[tex]\begin{gathered} \frac{\frac{1}{2}}{\frac{1}{3}}=\frac{x}{1} \\ \frac{\frac{1}{2}}{\frac{1}{3}}=x \end{gathered}[/tex]When you divide by a fraction, is the same as multiplying the dividend by the reciprocal fraction of the divisor, you can write the expression as follows:
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{3}{1}=x \\ \frac{1}{2}\cdot3=x \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]It will take him one and a half hours to complete the trip.
when your family gets together to exchange gifts things get a little crazy you counted a128 gifts 1/4 of them have your name on the tag 1/8 of them are for your cousin. Howw many gifts are not for you or your cousin?you came to the 128 gifts 1/4 of them have your name on the tag and 1/8 of them are for your cousins how many gifts are not for your cousins
Total gifts: 128
1/4 have your name. Multiply the total number of gifts by 1/4 to get the number of gifts that are for you:
Multiplication of a whole number and a fraction:
[tex]a\cdot\frac{b}{c}=\frac{a\cdot b}{c}[/tex]gifts that are for you:
[tex]128\cdot\frac{1}{4}=\frac{128\cdot1}{4}=\frac{128}{4}=32[/tex]1/8 of them are for your cousins. Multiply the total number of gifts by 1/8 to get the number of gifts that are for your cousins:
[tex]128\cdot\frac{1}{8}=\frac{128\cdot1}{8}=\frac{128}{8}=16[/tex]Then, subtract the number of gifts that are for you and the number of gifts that are for your cousins to get the answer of "How many gifts are not for you or your cousin?":
[tex]128-32-16=80[/tex] There are 80 gifts that are not for you or your cousins.To get the number of gifts that are not for your cousins substract 16 from the total of gifts:
[tex]128-16=112[/tex]There are 112 gifts that are not for your cousinsOne of these seven students will be selected at random. Which of these events describes students 1, 4, 5, 6, and 7 without including any of the other students?
ANSWER
Plays a fall sport or a spring sport
EXPLANATION
Student 1 plays a fall sport
Student 4 plays a fall sport and a winter sport
Student 5 plays a fall sport and a spring sport
Student 6 plays a spring sport
Stydent 7 plays a fall sport
Of these five students, 1, 4, 5 and 7 play a fall sport and student 6 plays a spring sport. So of these group each student plays a fall sport or a spring sport.
The temperature in Springfield at 10:00 am was 78 degrees F. During the day, it dropped to 56 degrees F. Write and solve an equation to find the decrease in temp.
Step 1. The initial temperature at 10:00 am was 78 degrees F, then there was a decrease in temperature and it dropped to 56 degrees F.
Let x be the decrease in temperature.
Step 2. The equation that will help us solve the problem is:
[tex]78-x=56[/tex]This is because 78 is the original temperature, and after a decrease of x degrees, the final temperature is 56.
Step 3. Now that we have the equation, we need to solve for x.
To solve for x, subtract 78 to both sides of the equation:
[tex]\begin{gathered} -x=56-78 \\ -x=-22 \\ \downarrow\downarrow \\ x=22 \end{gathered}[/tex]The decrease in temperature was 22 degrees.
Answer: The equation is
78-x=56
The solution
x=22
The sequence is arithmetic or geometric and the common difference or ratio is 5.
1. Arithmetic
2. common difference
1) Examining that sequence we can see that:
[tex]\begin{gathered} -6,-1,4,9 \\ -6+5=-1 \\ -1+5=4 \\ 4+5=9 \end{gathered}[/tex]So as we can see this sequence is an Arithmetic one, whose common difference is 5
2) That is the answer.
A map shows a garden with a width of 2 inches and a length of 6 inches. The map uses a scale of 1 inch for 10 yards. What is the actual length and width of the garden? Don't Forget the units.
Scale
1 inches = 10 yards
Width = 2 inches
2 * 10 = 20 yards
Length = 6 inches
6 * 10 = 60 yards
So, actual :
length = 60 yd
width = 20 yd
.........................answer explanation of another question shown on session....................
2 cake = 9 person
1 person = 2/9th cake
So,
45 person would take up:
45 * 2/9 = 10 cakes
I need help with this. Also when you’re done explaining it can you place the answer on top of the answer tab?
answer is option A
answer is option A
The figure represents a traffic island that has angles measuring 60°, 20°, and 100°. Match each angle with its correct measure. Use the red numbers and DRAG it to the appropriate angles of the triangle. Then Input your answers in the blanke. m 60 20* 100% m
Based on the given information you can notice:
angle M is greater than 90°, then, it is necessary m
angle P has a lower measure than angle N, moreover, both angles P and N are lower than 90°. Then, it is necessary mand m
mmmHello, I need some help with this homework question, please?HW Q24
Given:
[tex]h=-3t^2+147[/tex]Required:
We need to find the number of seconds will the plane be at a height of 20.25 feet.
Explanation:
Substitute h = 20.25 in the equation.
[tex]20.25=-3t^2+147[/tex]Subtract 147 from both sides of the equation.
[tex]20.25-147=-3t^2+147-147[/tex][tex]-126.75=-3t^2[/tex]Divide both sides of the equation by -3.
[tex]\frac{-126.75}{-3}=\frac{-3t^2}{-3}[/tex][tex]42.25=t^2[/tex]Take square root on both sides.
[tex]\pm\sqrt{42.25}=\sqrt{t^2}[/tex]Time is of positive value.
[tex]\sqrt{42.25}=t[/tex][tex]6.5=t[/tex]Final answer:
After 6.5 seconds the plane will be at a height of 20.25 feet.
A right square pyramid has the following dimensions: • The side length of the base is 5 inches. • The height is 9 inches. What is the volume of the pyramid? o 135 cubic inches O 115 cubic inches O 75 cubic incheso 90 cubic inches
Explanation:
Height = 9 inches
Length = 5 = inches
Area of the square is = l^2
Area = 5 x 5
Area = 25 square inches
Volume = 1/3
i dont understand how to get the answer of this problemThe question is: Using a protractor, draw a linear pair of angles in a 5:1 ratio.My teacher posted the answer key and the picture below is the answer I just don’t understand how to do the problem…
With a protractor, you can draw angles between 1° and 180°.
We need to draw a pair of angles in a 5:1 ratio, this means that the measure of one of the angles is 5 times the measure of the other. For example, if one angle is equal to 10° the other has to be equal to 50°.
In the image, your teacher suggested you draw a 30° angle and another equal to 150°
[tex]\frac{150}{30}=5[/tex]Then, the 5:1 ratio is preserved.
And remember that a linear pair of angles is the same as saying 'two adjacent angles that add up to 180°'
[tex]150+30=180[/tex]You can even write an equation to find out the angle.
[tex]\begin{gathered} 5x+x=180 \\ \Rightarrow6x=180 \\ \Rightarrow x=30 \end{gathered}[/tex]Then, one angle will be equal to 30° and the other 5*30°=150°
A car travels according to the table of values shown. What equation can be used topredict the distance (d) the car travels in a number of hours (h)?Hours1234Distance(miles)4590135180
SOLUTION
From the table, we can see that in 1 hour, the car covered 45 miles and in 2 hours, 90 miles, and in 3 hours 135 miles.
This means that the distance was increased by 45 miles for every additional 1 hour, that is
[tex]\begin{gathered} d=1hr\times45 \\ d=2hr\times(45+45) \\ d=3hr\times(45+45+45),\text{ that means } \\ d=45\times number\text{ of hours, since number of hours is h} \\ d=45\times h \\ d=45h \end{gathered}[/tex]Hence the first option d = 45h is the answer
- Which list represents the numbers arranged in descending order? :A)1.55x10^1,√155,155%,1/5,-15/3.B)√155,155%,1/5,1.55x10^1,-15/3.C)155x10^1,√155,155%,1/5,-15/3.D)-15/3,1.55x10^1,√155,155%,1/5.
Arranging in descending order means arraging the numbers frim the largest to the smallest.
Given the following values according to the options
1.55x10^1, √155, 155%, 1/5, -15/3.
Let us rewrite all the values as whole numbers and decimals
1.55x10^1 = 15.5
√155 = 12.45
155% = 155/100 = 1.55
1/5, = 0.2
-15/3 = -5
The largest value is 15.5, followed by 12.5 then 1.55, 0.2 and then -5th
The negative vakue there is the lowest value i.e -15/3
The arrangement from largest to smallest are;
1.55x10^1, √155, 155%, 1/5, -15/3
Option A is corect
Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P (6). Express your answer in exact form.P() =DOX
Sample space = {1, 2, 3, 4, 5, 6)
• P (1) = 1/6 or 16.67%
,• P (2) = 1/6 or 16.67%
,• P (3) = 1/6 or 16.67%
,• P (4) = 1/6 or 16.67%
,• P (5) = 1/6 or 16.67%
,• P (6) = You can complete it
The rectangular prism below has a base area of 38 units^2. and a height of 11.3 units. Find its volume.
Solution:
The volume of a rectangular prism is expressed as
[tex]volume\text{ = base area }\times\text{ height}[/tex]Given the rectangular prism below:
where
[tex]\begin{gathered} base\text{ area = 38 units}^2 \\ height\text{ = 11.3 units} \end{gathered}[/tex]The volume of the rectangular prism is evaluated as
[tex]\begin{gathered} volume\text{ = base area }\times\text{ height} \\ =38\text{ units}^2\times11.3\text{ units} \\ \Rightarrow volume\text{ = 429.4 units}^3 \end{gathered}[/tex]Hence, the volume of the rectangular prism is
[tex]429.4\text{ units}^3[/tex]The Third Floor residence of a building were Polled about whom they would vote for in the upcoming city election for comptroller. what are the sample amd population in this poll?the population is the registered voters in the building, the sample is the residence on the third floor.the population is the registered voters in the city. the sample is the residence of the third floorthe population is the registered voters in the city. the sample is the residence of the building the population is the registered voters of the building. the sample is the registered voters in the city
Answer:
The population is the registered voters in the city. the sample is the residence of the third floor
Explanation:
The population is the group that you want to know information about and the sample is a small group of the population that you select to collect the data.
In this case, the purpose is to know whom they would vote for the upcoming city election, so the population will be the registered voters in the city. Additionally, you only ask to the third floors residence of a building, then the sample will be the residence on the third floor.
So, the answer is:
The population is the registered voters in the city. the sample is the residence of the third floor
what is the original price of the tennis racquet if it is 30% off and the sale price is $21
sale price = $21
30% off is
let
x = original price
[tex]\begin{gathered} \frac{30}{100}x=21 \\ 30x=2100 \\ x=\frac{2100}{30} \\ x=\text{ \$70} \end{gathered}[/tex]The original price = $70
Suppose that the relation S is defined as follows.s={(-2,8), (5.-9).(-9,0).(-6, -6)}Give the domain and range of S.Write your answers using set notation.Domain=Range=
Remember that
The Domain is the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
The Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair)
In this problem we have
s={(-2,8), (5.-9).(-9,0).(-6, -6)}
therefore
The domain is [-9,-6,-2,5]The range is [-9,-6,0,8]Translate and solve: 82 less than a is at least -82 (express answer in interval notation)
Let's begin by identifying key information given to us:
82 less than a is given by:
[tex]82at least means greater than or equal to & is represented by the mathematical symbol ≥Putting this together, 82 less than a is at least -82 becomes:
[tex]82Question 1)A line with slope = 6 that passes through the point (3, 1) written in point-slope form is
The equation of a line in slope-intercept form is given as
[tex]y-y_1=m(x-x_1)[/tex]The slope of the line is 6
Hence, m = 6
Since the line passes through the point (3, 1)
Hence,
[tex]x_1=3,y_1=1[/tex]Substitute the values into the equation
This gives
[tex]y-1=6(x-3)[/tex]Simplify the equation
[tex]\begin{gathered} y-1=6x-18 \\ y=6x-18+1 \\ y=6x-17 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=6x-17[/tex]HHH NG DOJO 3 2 1 HHH -6-5-4-3-2-1 + 11 2 3 4 5 6 7 8 9 + -2 +-3 -4 OG ACN* -6 If this is the graph of f(x) = a*+h ( + k, then : O A. The domain is (h.), and the range is (-). B. The domain is (-0,), and the range is (k.co). C. The domain is (-0,9), and the range is (h.co). D. The domain is (h.), and the range is (-k.co). O
Given the graph of an exponential function;
[tex]f(x)=a^{(x+h)}+k[/tex]The domain of exponential functions is all real numbers.
Thus, the domain of the graph is;
[tex](-\infty,\infty)[/tex]
The range of a function is the set of outputs that satisfy the defined function.
Thus, the range of the graph is;
[tex](k,\infty)[/tex]CORRECT OPTION: B
Writing and Solving Systems Using Elimination: Tutorial? QuestionType the correct answer in each box. Use numerals instead of woSolve this system of equations using the elimination method.3x – 2y = 02x + y = 7
We are asked to solve a system of linear equations via the elimination method.
3 x - 2 y = 0
2 x + y = 7
in order to use elimination, we look into finding appropriat factors to use to multiply one (or both) of the equations, so that one of the variables can be eliminated just by adding the equations term by term, thus leaving us with an equation that contains only one unknown, and which we can easily solve.
Looking at our system, we select to multiply the second equation by "2",and that way, eliminate the term in
The sidewalk hazard marker is shaped like a pyramid,
with a height 2 centimeters greater than the length of
each side of its square base. The volume of the marker
is 297 cubic centimeters. What are the dimensions of
the sidewalk hazard marker?
Pyramid with a height 2 centimeters greater than the length of
each side of its square base. The volume of the marker is 297 cubic centimeters. Then dimensions length is 29.8 and height 31.8
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
The side of square base of pyramid x.
Height 2 centimeters greater than the length of each side of its square base=x+2
Volume of pyramid=297cubic centimeters
We have to calculate the dimensions
Volume=1/3 a²h
a is the side length.
h is height of pyramid.
297=x²(x+2)/3
891=x³+2x²
891=x²(x+2)
x²=891, x+2=891
x=29.8, x+2=891,x=889
Hence length of base the pyramid is 29.8 cm and height is 31.8cm
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ1
Write the inequality for this graph. Use x as your variable.
Notice that the points on the graph are all numbers greater than or equal to zero, therefore the given graph represents the following interval:
[tex]\lbrack0,\infty).[/tex]Zero is part of the graph because the circle is filled.
The above interval as an inequality is:
[tex]x\ge0.[/tex]Answer:
[tex]x\ge0.[/tex]Recently, more money 4u offered a annuity that pays 5.4% compounded monthly. If 878 is deposited into this annuity every month, how much is in the account after 8 years ? How much of this is interest
Step 1
State the formula for Future value compounded monthly.
[tex]FV=PMT(\frac{(1+i)^n-1)}{i})[/tex]where;
[tex]\begin{gathered} PMT=878 \\ i=\frac{5.4}{100\times12}=0.0045 \\ n=8\times12=96 \end{gathered}[/tex]Step 2
Find the future value
[tex]\begin{gathered} FV=878(\frac{(1+0.0045)^{96}-1^{}}{0.0045}) \\ FV=878(\frac{(1.0045)^{96^{}}-1}{0.0045}) \\ FV=\frac{473.1042497}{0.0045} \\ FV=105,134.2777 \\ FV\approx\text{ \$105134.28 to 2 decimal places} \end{gathered}[/tex]Find how much of the future value is interest
[tex]\text{Money paid in = 878}\times8\times12=\text{ \$84288}[/tex][tex]\begin{gathered} \text{Interest}=\text{ Future value - money paid in=}105134.27771-\text{ 84288}= \\ \text{Interest}=105134.27771-\text{ 84288}=20846.2777 \\ \text{Interest}\approx\text{\$}20846.28\text{ to 2 decimal places} \end{gathered}[/tex]Hence, the answers are;
How much is in the account after 8 years = $105134.28 to 2 decimal places
How much of this is interest = $20846.28 to 2 decimal places
in the figure below, two seconds are drawn to a circle from an exterior point E. Suppose that EZ = 16.8, EX = 14, and EW =35. Find XY.
Knowing that two secants are drawn to a circle from an exterior point, you need to use the Intersecting Secant Theorem.
Based on the Intersecting Secant Theorem, you can write the following equation:
[tex]EZ\cdot EW=EX\cdot EY[/tex]Knowing that:
[tex]\begin{gathered} EZ=16.8 \\ EX=14 \\ EW=35 \end{gathered}[/tex]Substitute those values into the equation:
[tex](16.8)(35)=(14)\cdot EY[/tex]Solve for EY:
[tex]\begin{gathered} 588=14EY \\ EY=\frac{588}{14} \\ EY=42 \end{gathered}[/tex]Notice that:
[tex]EY=EX+XY[/tex]Then you can substitute values and solve for XY:
[tex]\begin{gathered} 42=14+XY \\ 42-14=XY \\ XY=28 \end{gathered}[/tex]The answer is:
[tex]XY=28[/tex]in order to build a shee you need to build 6 inches of height for a base that is 26 inches long. What is the height of a shed thats is 156 inches long?Part A: What id the equation that represents this relationship y= blankPart B: A shed that is 156 inches long is blank inches high
The sheds must be similar so we han have the relation:
[tex]\frac{y}{6}=\frac{156}{26}[/tex]So we can solve for y to have an expression so:
[tex]y=\frac{6\cdot156}{26}[/tex]and we can solve it so:
[tex]y=36[/tex]So the shed that is 156 inches long has a high of 36 inches
Graph the quadratic function f(x) = 2(x - 3)2 - 2 and select all of the following which are true.maximum at (-3,-2)minimum at (3,-2)x-intercept at (2,0)x-intercept at (4,0)y-intercept at (0, -16)
Graph:
By looking at the graph we can see that:
It opens upwards, so it has a minimum at (3,-2)
I crosses the x axis at x=2 and x=4
x- intercepts at (2,0) and (4,0)
It doesn't cross the y axis
12. Derek scored a total of 42 points in the first 4 basketballgames. If he continues to score at this rate, how manypoints will he score during the entire 18-game season?
Given data:
The numbers of points scored in 4 games are 42.
The expression for the given statement is,
[tex]\begin{gathered} 4\text{ games= 42 points} \\ 1\text{ game = 10.5 points} \end{gathered}[/tex]Multiply the above expression by 18 on both sides.
[tex]\begin{gathered} 18(1\text{ game) =18(10.5 points)} \\ 18\text{ games =189 points} \end{gathered}[/tex]Thus, in 18 games 189 points achieved.
Based on the 2017 season, the Houston Astros have a winning percentage of 623. Use the binomial model to find the probability that the Astros will win 4 of their next 6 games. P (1) = ( z Xn-3) p'ai O A 12.4% O B. 24.7% O C. 32.1% O D. 62.3%