We have to find how many students were in each bus.
We can call this quantity "x".
The total number of students is 317.
This quantity can be divided in the number of students that rode in cars, 22, and the rest went in 5 buses.
The quantity that rode in bus can be expressed as 5x.
Then we can write:
[tex]22+5x=317[/tex]We can solve this as:
[tex]\begin{gathered} 22+5x=317 \\ 5x=317-22 \\ 5x=295 \\ x=\frac{295}{5} \\ x=59 \end{gathered}[/tex]Answer: there were 59 students in each bus.
Given the lines below, create a line that is parallel, one that is perpendicular, and one that is neither. Y = -6Parallel: Perpendicular: Neither:
Given:
[tex]y=-6[/tex]The slope of the given line is zero.
a) parallel line: Parallel lines have the same slope. Any line whose slope is x=zero will be parallel to line y=-6.
So, one equation can be,
[tex]y=-2[/tex]2) Perpendicular line
Clearly the line y=-6 is the horizontal line having a slope of 0.
So, the line perpendicular to this line will be a verticle line with an undefined slope.
And its equation is of the form x = a.
The equation can be,
[tex]x=2[/tex]c) The lines which are neither parallel nor perpendicular will be just the intersecting lines.
The equation can be,
[tex]y=x+1[/tex]Cyrus is hosting a dinner to celebrate Nowruz, the Perian New Year. His groceries cost $150 before he uses a 10% off coupon. He also order $50 worth of flowers Sales tax on the flowers in 6.254%. What is the total amount Cyrus spends?
Data:
Groceries: $150
10% off
Flowers: $50
Sales tax on the flowers: 6.254%
To find the total amount:
1. Find the 10% of 150:
[tex]150\cdot\frac{10}{100}=15[/tex]2. As the coupon is 10% off you substract the 10% of $150:
[tex]150-15=135[/tex]For the groceries Cyrus pays $135
3. Find the 6.254% of 50:
[tex]50\cdot\frac{6.254}{100}=3.13[/tex]4. As the 6.254% is sales tax you add it to the $50:
[tex]50+3.127=53.13[/tex]For the flowers Cyrus pays $53.13
The total amount Cyrus spends is: $188.13[tex]135+53.127=188.13[/tex]Solve the following system of linear equations by graphing:4x + 4y = 2010x + 2y = 18
one solution: (1, 4)
The equations:
y = -x + 5
y = -5x + 9
Explanation:[tex]\begin{gathered} \text{Given equations:} \\ 4x+4y=20\text{ }\ldots(1) \\ 10x+2y=18\text{ }\ldots(2) \end{gathered}[/tex]To plot the graphs, we can assign values to x. The we get the corresponding values of y for each of the equation.
Rewritting the two equations by making y the subject of formula:
[tex]\begin{gathered} 4x+4y=20 \\ \text{divide through by 4:} \\ x\text{ + y = 5} \\ y\text{ = -x + 5} \end{gathered}[/tex][tex]\begin{gathered} 10x+2y=18 \\ \text{divide through by 2:} \\ 5x\text{ + y = 9} \\ y\text{ = -5x + 9} \end{gathered}[/tex]Plotting the graphs:
The point of intersection of the graphs is the solution.
There is one solution: (1, 4)
Use Pascal's Triangle to expand the binomial. (d-3)^6
Using pascal triangle
(d-3)^6
Expoenent 6 has a coeffient of;
1 6 15 20 15 6 1
Hence;
[tex]d^6-6(d)^5(3)+15(d)^4(3)^2-20(d)^3(3)^3+15(d)^2(3)^4-6(d)(3)^5+3^6[/tex]Two things to note here is that;
-There is a minus sign in-between the numbers in the bracket, hence we alternate the sign starting with positive
-secondly as the power of the first variable decreases the power of the second digit increases
We can further simplify;
[tex]d^{6\text{ }}-6d^5(3)+15(d)^4(9)^{}-20d^3(27)+15d^2(81)-6d(243)+729[/tex]We will still simplify to give:
[tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d\text{ + 729}[/tex]Answer:
The Binomial Theorem Quick Check:
1. [tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d+729[/tex]
2. [tex]s^5+15s^4v+90s^3v^2+270s^2v^3+405sv^4+243v^5[/tex]
3. [tex]-64b^3[/tex]
100% 3/3
You're Welcome! A brainliest would help me alot. ‿
Rose curves are characterized by equations of the form r=acos(nθ) or r=asin(nθ), a≠0. If n≠0 is even, the rose has __________ petals; if n≠±1 is odd, the rose has __________ petals.
We have that:
If n is an even integer, then the rose will have 2n petals.
If n is an odd integer, then the rose will have n petals.
Answer:
Rose curves are characterized by equations of the form r=acos(nθ) or r=asin(nθ), a≠0. If n≠0 is even, the rose has 2n petals; if n≠±1 is odd, the rose has n petals.
Please help me with the question and explain your work! 16 through 19 thank you please please please help
We have the following:
A.
First we find the slope of the line with the following points:
(0, 3) and (5,0)
[tex]m=\frac{0-3}{5-0}=-\frac{3}{5}[/tex]now, for b, with the point (0,3)
[tex]\begin{gathered} 3=-\frac{3}{5}\cdot0+b \\ b=3 \end{gathered}[/tex]The equation is:
[tex]y=-\frac{3}{5}x+3[/tex]B.
The area is:
[tex]\begin{gathered} A=\frac{AC\cdot CB}{2} \\ A=\frac{3\cdot5}{2}=\frac{15}{2} \\ A=7.5 \end{gathered}[/tex]The area is 7.5 square units
for, perimeter:
[tex]\begin{gathered} p=AC+CB+AB \\ AB^2=AC^2+CB^2 \\ AB^2=3^2+5^2=9+25=34 \\ AB=\sqrt[]{34} \\ p=3+5+\sqrt[]{34} \\ p=13.83 \end{gathered}[/tex]The perimeter is 13.83 units
C.
when two lines are perpendicular they fulfill the following
[tex]m_1\cdot m_2=-1[/tex]therefore,
[tex]\begin{gathered} -\frac{3}{5}\cdot m_2=-1 \\ m_2=\frac{5}{3} \end{gathered}[/tex]Therefore, the equation is:
[tex]y=\frac{5}{3}x+3[/tex]what decimals are between 0.82 and 0.83
Answer:
0.82 and 0.83
Anthropologists use a linear model that relates femur length to height. The model allows an anthropologist todetermine the height of an individual when only a partial skeleton (including the femur) is found in this problem, wefind the model by analyzing the data on femur length and height for the eight males given in the tableFemur length (cm)49.948.646.345.844.343.639.738.9Height (cm)177.5174.6165.6164.7165.3164.6155.8156.71.Which scatterplot best matches the given data?A.B.2.What is the correlation coefficient for this data?
For the scatter plot (part 1), you should have gotten something like this.
Notice that, in general, the greater the femur length is, the taller the person is. Therefore, the relation between those two quantities has the form
[tex]Y=mX+b,m>0[/tex]And, the correlation coefficient is
[tex]r=\frac{\sum ^{\square}_{\square}(x_i-\bar{x})(y_i-\bar{y})}{\sqrt[]{\sum ^{\square}_{\square}(x_i-\bar{x})^2\sum ^{\square}_{\square}(y_i-y)^2}}[/tex]In our case,
[tex]\begin{gathered} \bar{x}=\frac{1}{8}(49.9+48.6+46.3+45.8+44.3+43.6+39.7+38.9)=44.6375 \\ \bar{y}=\frac{1}{8}(177.5+174.6+165.6+164.7+165.3+164.6+155.8+156.7)=165.6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \sum ^{\square}_{}(x_i-\bar{x})(y_i-\bar{y}_{})=197.83 \\ \end{gathered}[/tex]and
[tex]\begin{gathered} \sum ^{\square}_{\square}(x_i-\bar{x})=105.9987 \\ \sum ^{\square}_{\square}(y_i-\bar{y})=399.76 \end{gathered}[/tex]Finally,
[tex]\Rightarrow r=\frac{197.83}{\sqrt[]{(105.9987)(399.76)}}=0.961[/tex]Thus, the correlation coefficient is equal to 0.961
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
r=8 cm
pi=3.14
substitute the given values in the formula
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot8^3 \\ V=2,143.6\text{ cm\textasciicircum{}3} \end{gathered}[/tex]answer is
2,143.6 cubic centimetersCombo 1Combo 2Combo 33 glazed5 glazed4 glazed4 cream filled6 cream filled4 cream filled5 chocolate1 chocolate4 chocolate$38$32$36a)Write a system to represent this situation. Use g for glazed donuts, f for cream filled donuts, and c for chocolate donuts.b)Solve the system ALGEBRAICALLY to find the price of each donuts.
We will use the following variables :
g for glazed
f for cream filled donuts
c for chocolate donuts
So, the equation for combo 1
3 g + 4 f + 5 c = $38
The equation for combo 2:
5 g + 6 f + c = $32
The equation for combo 3:
4 g + 4 f + 4 c = $36
So, the system of equations are:
3 g + 4 f + 5 c = 38 (1)
5 g + 6 f + c = 32 (2)
4 g + 4 f + 4 c = 36 (3)
B) Now, we need to solve the system of equations:
From equation 3:
4 g + 4 f + 4c = 36
divide all terms by 4
So, g + f + c = 9
Solve for c:
c = 9 - g - f
Substitute with the value of c at the equations (1)
At (1):
3 g + 4 f + 5 (9 - g - f) = 38
3g + 4f + 45 - 5g - 5f = 38
-2g - f = 38 - 45
-2g - f = -7
Multiply all terms by -1
2g + f = 7
Solve for f
f = 7 - 2g
Substitute with f at the equation of c
c = 9 - g - (7 - 2g)
c = 9 - g - 7 + 2g
c = g + 2
So, we have reached to :
f = 7 - 2g and c = g + 2
substitute with f and c at the equation (2)
5g + 6f + c = 32
5g + 6 (7 - 2g) + g + 2 = 32
solve for g
5g + 42 - 12 g + g + 2 = 32
5g - 12g + g = 32 - 42 - 2
-6g = -12
Divide both sides by -2
g = -12/-6 = 2
f = 7 - 2g = 7 - 2 * 2 = 7 - 4 = 3
c = g + 2 = 2 + 2 = 4
So, the cost of glazed = $2
The cost of cream filled = $3
The cost of chocolate = $4
IF AB = (2x + 23). BC = (12 + 7x), and CD = 19 - 9x), find AD.
The addition of length of each line segment gives the value of AD.
[tex]\begin{gathered} \text{From the number line, AB+BC+CD=AD} \\ AD=(2x+23)+(12+7x)+(19-9x)=2x+7x-9x+23+12+19=54 \end{gathered}[/tex]The value of AD is 54.
students at a local school were asked. “about how many hours do you spend on homework each week “?The table shows the results of the survey . classify the statement below as true or false .more students study for 5 to 6 hours than for 1 to 2 hours
From the table:
The number of students that study for 5 to 6 hours = 109
The number of students that study for 1 to 2 hours = 142
Since 109 is less than 142:
The statement is False because 109 students study for 5 to 6 hours and 142 students study for 1 to 2 hours.
5+3(-2x+1)=16 I need help
Given:
5 + 3(-2x + 1) = 16
Let's solve for x.
• Step 1:
Use distributive property to expand the parenthesis
5 + 3(-2x) + 3(1) = 16
5 - 6x + 3 = 16
• Step 2:
Combine like terms
-6x + 3 + 5 = 16
-6x + 8 = 16
• Step 3:
Subtract 8 from both sides
-6x + 8 - 8 = 16 - 8
-6x = 8
• Step 4:
Divide both sides by -6
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{8}{-6} \\ \\ x=-\frac{4}{3} \end{gathered}[/tex]ANSWER:
[tex]-\frac{4}{3}[/tex]•
QThe image of point A (3, 4) under translation Tis A' (-1,6). What is the translation rule? worth 50 points guy's can someone please give me an answer really quick please!!!
Here, we want to find the translation rule
Dr. Walton is studying a bacterial colony with a population of 77,000 bacteria. The colony is growing 15% per hour. How many bacteria will the colony contain in 3 hours?
The colony will contain 117,107 bacteria in 3 hours
Here, we start by writing an exponential function that can represent the question
We have this as;
[tex]N=I(1+r)^t[/tex]N is the number of bacteria at a particular time t
I is the initial number of bacteria which is 77,000
r is the growth rate which is 15% = 15/100 = 0.15
t is the time in hours = 3
Substituting these values, we have it that;
[tex]\begin{gathered} N=77,000(1+0.15)^3 \\ N=77,000(1.15)^3 \\ N\text{ = 117,107} \end{gathered}[/tex]This answer is given to the nearest whole number
Find each value if f(x) = 2x - 1 and g(x) = 2 - x2.9. f(0)
ANSWER
f(0) = -1
EXPLANATION
We just have to replace x by 0 into f(x):
[tex]\begin{gathered} f(x)=2x-1 \\ f(0)=2\cdot0-1 \\ f(0)=0-1 \\ f(0)=-1 \end{gathered}[/tex]what 3 1/4 - 1 3/8 equal?
Answer : 1 7/8
Given that: 3 1/4 - 1 3/8
Step 1: Convert the mixed fraction into an improper fraction
3 1/4 = (4 x 3) + 1 / 4
3 1/4 = 12 + 1 / 4
3 1/4 = 13/4
1 3/8 = (8 x 1) + 3 / 8
1 3/8 = 8 + 3 / 8
1 3/8 = 11/8
13/4 - 11/8
The common denominator is 8
2 x 13 - 11 x 1 / 8
26 - 11 / 8
15/8
1 7/8
Therefore, the answer is 1 7/8
How much sugar is in a 340 gram mixture if you know the mixture is 50%sugar?
We got 340 gram mixture. The 50% of it is sugar, so:
[tex]\frac{50}{100}\cdot340=170[/tex]Then, there are 170g of sugar.
20 4/5 whats the decimal number
20 4/5
it means 20 integers and 4/5
4/5 = 0.8
so the number 20 4/5 is equal to 20.8
answer: 20.8
20 7/8 is 20 integers and 7/8
7/8 = 0.875
so 20 7/8 is equal to 20.875
Katherine is speeding in her car, and sees a parked police car on the side of the road right next to her at t=0 seconds. She immediately decelerates, but the police car accelerates to catch up with her (assume the two cars are going in the same direction in parallel paths). The distance that Katherine has traveled in feet after t seconds can be modeled by the equation d(t) = 150 + 75t - 1.2t^2. The distance that the police car travels after t seconds can be modeled by the equation d(t) = 4t^2.a) How long will it take the police car to catch up to Katherine?b) How many feet has Katherine traveled from the time she saw the police car until the police car catches up to her?
When the police car catches up Katherine their distances from the point at t=0 are the same, then we can find the time that it takes them to advance that distance by making the expression that models the distance of Katherine and the equation for the distance of the police equal, like this:
[tex]\begin{gathered} 150+75t-1.2t^2=4t^2 \\ 150+75t-5.2t^2=0 \end{gathered}[/tex]We know that for an equation of the form at^2+bt+c=0 the value of t can be calculated with the quadratic formula, for this case a= -5.2, b=75 and c=150, then applying the quadratic formula we get:
[tex]undefined[/tex]A pizza place offers ten different toppings. A special is a pizza with any three different toppings. How many different types of specials are offered?
As given by the question
There are given that the total of 10 different topping
Now,
According to the question:
There is also talk about 3 different pizzas.
So,
The three different toppings from the 10 different toppings:
[tex]10C_3=\frac{10!}{3!(10-3)!}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10!}{3!(10-3)!} \\ 10C_3=\frac{10!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8\times7!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8}{3\times2\times1} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10\times9\times8}{3\times2\times1} \\ 10C_3=10\times3\times4 \\ 10C_3=120 \end{gathered}[/tex]Hence, 120 different pizzas are possible.
what are the coordinates of the library A (3,4)b. (4,3)c..(2,1)d.(1,2
To determine the coordinates of the library, for the x-coordinate, you have to draw a vertical line from the library to the x-axis and read where it intersects the x-axis. And to determine the y-coordinate you have to draw a horizontal line from the position of the library towards the y-axis, and read where the line intersects the y-axis:
The x-coordinate is 4 and the y-coordinate is 3, so the coordinates of the library are (4,3)
find an equation of the line having the given slope and containing the given point . Slope -2; through (6,-9) . type answer in slope-intercept form .
Given:
The slope of the line is m = -2.
The line passes throught the point (6,-9).
The objective is to find the equation of line.
Explanation:
Consider the point as,
[tex](x_1,y_1)=(6,-9)[/tex]The general equation to find the equation of line in slope intercept form is,
[tex]y-y_1=m(x-x_1)[/tex]Substitution:
On plugging the given values in the general equation,
[tex]\begin{gathered} y-(-9)=-2(x-6) \\ y+9=-2x+12 \\ y=-2x+12-9 \\ y=-2x+3 \end{gathered}[/tex]Here, slope of the line is -2 and y- intercept is 3.
Hence, the equation of the line in slope intercept form is y = -2x + 3.
Find the value of the ratio using the term sequence 5, 15, 45 , 135, ...
To find the ratio, we just have to divide the second term by the first term.
[tex]\frac{15}{5}=3[/tex]Therefore, the ratio of the sequence is 3.Notice that the given sequence is geometrical because we have to multiply each term with 3 to get each new term.
Pure acid is to be added to a 20% acid solution to obtain 44 L of a 40% acid solution.What amounts of each should be used?
Let:
x be the liters of 20% acid solution.
y be the liters of pure acid solution.
To find x and y, follow the steps below.
Step 01: Write an equation for the number of liters.
The number of liters of the solution is 44, which is the sum of x and y.
[tex]x+y=44[/tex]Step 02: Isolate y in the equation above.
To do it, subtract x from both sides.
[tex]\begin{gathered} x+y-x=44-x \\ y=44-x \end{gathered}[/tex]Step 03: Write an equation that expresses the total of acid.
The total of acid is 0.4*44, which is equal to 1y plus 0.2x.
[tex]\begin{gathered} 0.4\cdot44=1\cdot y+0.2\cdot x \\ 17.6=y+0.2x \end{gathered}[/tex]Step 04: Substitute y by 44 - x in the equation above and isolate x.
[tex]\begin{gathered} 17.6=44-x+0.2x \\ 17.6=44-0.8x \end{gathered}[/tex]To isolate x, subtract 44 from both sides.
[tex]\begin{gathered} 17.6-44=44-0.8x-44 \\ -26.4=-0.8x \\ \end{gathered}[/tex]Now, divide both sides by -0.8.
[tex]\begin{gathered} \frac{-26.4}{-0.8}=\frac{-0.8}{-0.8}x \\ 33=x \end{gathered}[/tex]Step 05: Use the equation from step 2 to find y.
[tex]\begin{gathered} y=44-x \\ y=44-33 \\ y=11 \end{gathered}[/tex]Answer:
x is the liters of 20% acid solution = 33 L.
y is the liters of pure acid solution = 11 L.
please help me ASAP!!!
Fill in only the blanks. (Whatever that has an answer like the domain don’t do it)only do the empty blanks
From the graph, we can conclude:
[tex]Range\colon(-\infty,1)[/tex]As:
[tex]\begin{gathered} x\to0,f(x)\to-\infty \\ x\to\infty,f(x)\to1 \end{gathered}[/tex]x-intercept:
[tex](1,0)[/tex]Asymptote:
Vertical asymptote:
[tex]x=0[/tex]Horizontal asymptote:
[tex]y=1[/tex]Sketch a quick diagram of how all the quadrilaterals relate to one another
The diagram of various types of quadrilaterals are attached below.
A quadrilateral is polygon that has 4 sides.
Firstly we have a parallelogram which has both pairs of opposite side equal and parallel.
Second we have a trapezium where only one pair of side is parallels but other pair is not parallel.
A rhombus is a parallelogram whose all sides are equal but the angles are not right angles.
A rectangle has all angles 90° but the opposite sides are equal but adjacent sides are not equal.
A square has all sides equal and all angles 90° .
A kite has only 2 pairs of adjacent sides equal.
to learn more about quadrilaterals visit:
https://brainly.com/question/13805601
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Help me solve for equation 6x+3=33
Given:
[tex]6x+3=33[/tex]is given.
Required:
We need to solve this equation.
Explanation:
Here an equation given as
[tex]6x+3=33[/tex]now add both side negative 3 and we get
[tex]\begin{gathered} 6x+3-3=33-3 \\ 6x=30 \end{gathered}[/tex]now multiply both side with inverse 6
[tex]\begin{gathered} \frac{1}{6}*6x=30*\frac{1}{6} \\ x=5 \end{gathered}[/tex]Final answer:
Solution of given equation is
[tex]x=5[/tex]
Suppose Piper eats out twice a week 15% of the time, she eats out once a week 35% of the time, and she does not eat out any time during the week 50% of the time.What is the expected value for the number of times Piper eats out during the week? Round your answer to the nearest hundredth if needed.
Solution
We are given
Probability of eating out twice in a week = 15% = 0.15
Probability of eating out once in a week = 35% = 0.35
Probability of not eating out in a week = 50% = 0.50
Let X be a random variable of the number of times Piper eats out in a week
So we have the table
Note: The Formula For finding the Expected value E(X) is given by
[tex]E(X)=\sum ^{}_{}xp(x)[/tex]Substituting we get
[tex]\begin{gathered} E(X)=0(0.50)+1(0.35)+2(0.15) \\ E(X)=0+0.35+0.30 \\ E(X)=0.65 \end{gathered}[/tex]Therefore, the expected value is
[tex]E(X)=0.65[/tex]