hello
to solve this question, we need to write down details we have first in order to take some key facts into consideration.
1 bus (70 students + 6 chaperones) = $1300
1 van (10 students +1 chaperone) = $80
we have to take into consideration that the trip can only accomodate only 60 chaperone and also find the least expensive options to take.
the total number of students in senior class = 630 students
the best option would be to pick 7 buses and 15 vans
7 buses would be
[tex]\begin{gathered} 7\text{ buses} \\ 70\times7=490\text{ students} \end{gathered}[/tex]7 buses would accomodate 490 students and will require
[tex]7(\text{buses)}\times6\text{ chaperones }=42[/tex]7 buses will accomodate 490 students and would require 42 chaperones.
now we would need at least 14 vans to accomodate the remaining students.
[tex]\begin{gathered} 14\text{ buses} \\ 10(\text{students)}\times14=140\text{ students} \end{gathered}[/tex]14 vans would require a total of 14 chaperones
[tex]\begin{gathered} 7\text{ buses}=490\text{ students and 42 chaperones} \\ 14\text{ vans}=140\text{ students and 14 chaperones} \\ \text{total number of students = 630 students} \\ \text{total number of chaperones required = 42 + 14 =56} \end{gathered}[/tex]now we can calculate the cost of the journey
[tex]\begin{gathered} 1\text{ bus costs =\$1300} \\ 7\text{ buses = 7}\times\text{ \$1300}=\text{ \$9,100} \\ 1\text{ van costs =\$80} \\ 14\text{ vans will cost = 14}\times\text{ \$80}=\text{ \$1,120} \\ \text{total costs = \$9,100 + \$1,120}=\text{ \$10,220} \end{gathered}[/tex]from the calculations above, the minimal cost of the journey is $10,220 and
Directions: If JK is tangent to circle L, find x
If line JK is tangent to the circle L, the triangle JKM is a right triangle. Then, you can calculate the line JM by using the Pythagorean theorem, as follow:
KM² = KJ² + JM²
KJ = 7
KM = 25
Solve the equation for JM and replace the values of the other parameters:
JM = √(KM² - KJ²)
JM = √((25)² - (7)²)
JM = √(625 - 49)
JM =√(576)
JM = 24
next, consider that line JM is the diameter of the circle
equation (y= 5/7 x +10)which equation is parallel to the above equation and passes through the point (35,30)?- y = 5/7x + 5- y = 5/7x + 79- y = 5/7x + 10
the original equation is:
[tex]y=\frac{5}{7}x+10[/tex]So we know that a parallel line will have the same slope, so we can calculate the intercept with the slope and the coordinate (35,30)
[tex]undefined[/tex]A rectangular plot measures 12 m by 5 m. A path of constant width runs along one side and one end. If the total area of the plot and the path is 120 m², find the width of the path.
Answer:
the width of the path is 24m²
Solve -5x² = -25 using any method: Round your solutions to the nearest hundredth.
Solution of the given expression -5x² = -25 to the nearest hundredth is given by ±2.24.
As given in the question,
Given expression is equal to :
-5x² = -25
Solution of the given expression -5x² = -25 to the nearest hundredth
By dividing both the side by -5 of the given expression we get,
-5x²/-5 = -25 / -5
⇒ x² = 5
Take square root both the side of the given expression we have,
√x² = √5
⇒ x = ± 2.23606...
⇒ x = ± 2.24 (round off to the nearest hundredth)
Therefore, solution of the given expression -5x² = -25 to the nearest hundredth is given by ±2.24.
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-2(9x - 1)= -(x - 9) - 7x
Answer:
x=7/10
Step-by-step explanation:
Use distributive property to simplify.
-18x + 2 = -x + 9 - 7x
Simplify like terms.
-18x + 2 = 9 - 8x
Add 18x on both sides.
10x+9=2
Subtract 9 on both sides.
10x=7
Divide by 10 on both sides.
x=7/10
Which of the following doesnot represent the slope of the line1: 8/42: 4/23:1/24: 2
We can express the slope of a line as the ratio between the variation in y, in the vertical axis, and the variation in x, in the horizontal axis.
We can use any pair of points in the line to calculate the slope.
If we use the pair of points that form the smaller triangle, we get:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{4}{2}=2[/tex]We can also see that the bigger triangle will give a slope of m = 8/4 = 2, an equivalent result as expected.
Then, we can write the slope as 4/2, 8/4 and 2.
The only value that does not correspond to the slope of this line is 1/2.
Answer: 1/2 [Option 3]
3. Disney on Ice is traveling to Chicago to perform. The revenue from their ticketsales is a function of the ticket price, x, and can be modeled with (x - 3)(450 – 3x).What are the ticket prices at which Disney on Ice would make no money at all?Type Here:Explain or show your reasoning.Type Here:
They would not earn money when the function is equal or less to 0
then we equal 0
[tex](x-3)(450-3x)\leq0\text{ }[/tex]we will have two answers when clear x
[tex]\begin{gathered} (x_1-3)\leq0 \\ x_1\leq3 \\ (450-3x_2)\text{ }\leq\text{0} \\ 450\leq3x_2 \\ x_2\ge\frac{450}{3} \\ x_2\ge150 \end{gathered}[/tex]they won't make money when the ticket price is equal or less than 3 or when the ticket price is equal or greater than 150
the correct expression for not making money is :
[tex](-\infty,3\rbrack\text{ }\lbrack150,\infty)[/tex]Can u please double check I answered this correctly! The first time I got 4pi. The second I got 2pi…
Given:
Given a table of values of a cosine function.
Required: Period of the function
Explanation:
The maximum of the cosine function occurs at the points
[tex]x=-2\pi\text{ and }x=2\pi[/tex]The period of the function is the modulus of the difference of the consecutive values at which the function attains maximum/minimum.
[tex]\begin{gathered} \text{ Period=}|-2\pi-2\pi| \\ =|-4\pi| \\ =4\pi \end{gathered}[/tex]Final Answer: The period of the given cosine function f(x) is
[tex]4\pi[/tex]Paul and Brian win some money and share it in the ratio 4:1. Paul gets £24 more than Brian.
How much did they get altogether?
Money shared by Paul and Brian altogether in a win is $40.
What is definition of the term equation?In its most basic form, an equation is arithmetic declaration that demonstrates that two formulas are equal. For example, 53x + 5 = 14 is an equation in which the expressions 53x + 5 and 14 are separated by a 'equal' sign. In mathematics, a most basic and simple arithmetical equations comprise of one or even more variables.For the given question;
Let the money shared by Brian be x.
The, the money shared by the Paul is; x + 24.
The ratio of the money of Paul and Brian is 4:1.
(x + 24)/x = 4/1
Cross multiplying.
x + 24 = 4x
3x = 24
x = 8 (Brian's shared money)
Paul' shared money = 8 + 24 = 32.
Total money = 32 + 8 = $40
Thus, money shared by Paul and Brian altogether in a win is $40.
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can you help me with my work
Keke, this is the solution:
f (x) = 50 (0.6) ^x
Height of the first bounce = 50 (0.6)
Height of the first bounce = 30 feet
Height of the second bounce = 50 (0.6)²
Height of the second bounce = 50 * 0.36
Height of the second bounce = 18 feet
Height of the third bounce = 50 (0.6) ^3
Height of the third bounce = 50 * 0.216
Height of the third bounce = 10.8 feet
Use long division to divide. 340 ÷ 5.
MARK BRAINLIST AND I NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
68
5 can go into 3 0 times so skip that, 5 can go into 34 6 times, put a 6 on top 6×5=30 34-30=4 bring the 0 down 5 can go into 40 8 times so put an 8 beside the 6 8×5=40 40-40=0
Hope this is understandable and helps
Answer:
Hope it helps you
Step-by-step explanation:
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If 6-foot-tall Madeleine casts an 108-inch shadow, how tall is her friend if, at the same time, his shadow is 1.5 shorter than hers? Explain.
Given:
There are given that the 6-foot-tall Madeleine casts a 108-inch shadow.
Explanation:
Madelene's height is 6 ft.
And,
The height of her shadow is represented as 108 inches.
According to the question:
Her friend shadow is 1.5 feet, i,e 18 inches, shorter.
So,
The friend's shadow is:
[tex](108-18)in=90in[/tex]So,
We have following equivalent ratio:
[tex]\frac{6}{108}=\frac{h}{90}[/tex]Then,
[tex]\begin{gathered} \frac{6}{108}=\frac{h}{90} \\ 540=108\times h \\ h=\frac{540}{108} \\ h=5 \end{gathered}[/tex]Final answer:
Hence, her friend's height is 5 feet.
There are 5 bacteria in a petri dish at the start of
an experiment. This type of bacteria doubles
every 20 minutes.
Find the number of bacteria after 4 hours.
•
40
•
10,240
•
20,480
40,960
Answer:
20,480
Step-by-step explanation:
Samantha Jones is going on vacation and plans to rent a full size car fromSpeedy Rent-A-Car. She has a budget of $75 per day for car rental. What isthe maximum distance Samantha can drive in one day and still stay within herbudget?
According to the given data we have the following:
Samantha has rent a full size car fromSpeedy Rent-A-Car
Budget= $75 per day
Because this is a full size car the cost is 22.95 plus 0.15 per mile
So, if X is the maximum distance samanta
If f(x)f(x) is an exponential function where f(-3.5)=12f(−3.5)=12 and f(6)=44f(6)=44, then find the value of f(1)f(1), to the nearest hundredth.
The value of the exponential function f(1) is 3.88
Given,
The exponential function f(x)
f(-3.5) = 12
f(6) = 44
We have to find the value of f(1).
Exponential function;
y = abˣ
Where,
a is the initial value
b is the rate of change
Here,
f(-3.5) = 12
y = abˣ
12 = ab⁻³°⁵
a = 12/b⁻³°⁵
Next,
f(6) = 44
y = abˣ
44 = ab⁶
We have a = 12/b⁻³°⁵
Then,
44 = 12/b⁻³°⁵ × b⁶
b²°⁵ =44/12
2.5√b²°⁵ = 2.5√44/12
b = (44/12)^1/2.5
b = 1.68
Then,
44 = ab⁶
a = 44/b⁶
a = 44/ 1.68⁶
a = 1.96
Here,
y = 1.96 × 1.68ˣ
Here,
x = 1
Then,
y = 1.96 × 1.68
y = 3.88
That is,
The value of the exponential function f(1) is 3.88
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find the average rate of change of the given function on the interval [1,5] g(x)=-3x^2+x+1
=====================================================
Explanation:
Plug in x = 1 which is the left endpoint of the interval [1,5] aka [tex]1 \le \text{x} \le 5[/tex]
g(x)=-3x^2+x+1
g(1)=-3(1)^2+1+1
g(1) = -1
Then plug in x = 5 which is the right endpoint of that interval mentioned.
g(x) = -3x^2+x+1
g(5) = -3(5)^2+5+1
g(5) = -69
---------
AROC = average rate of change
The AROC of g(x) from x = a to x = b is given by this formula
[tex]\text{AROC} = \frac{g(b)-g(a)}{b-a}\\\\[/tex]
Plug in a = 1 and b = 5. Then simplify.
[tex]\text{AROC} = \frac{g(b)-g(a)}{b-a}\\\\\text{AROC} = \frac{g(5)-g(1)}{5-1}\\\\\text{AROC} = \frac{-69-(-1)}{5-1}\\\\\text{AROC} = \frac{-69+1}{5-1}\\\\\text{AROC} = \frac{-68}{4}\\\\\text{AROC} = -17\\\\[/tex]
The average rate of change on the interval [1, 5] is -17
This is the same as finding the slope through the lines (1,-1) and (5,-69). Notice the form and structure of the AROC formula mimics the slope formula.
The g(b)-g(a) portion mimics y2-y1 in the numerator.
The b-a portion mimics x2-x1 in the denominator.
URGET PLEASE HELP!!!!!!!!!!!!!!!!!
It is the bottom left one
It is an absolute value graph, so the line should be a y = x graph but all y values are positive.
the bottom left one shows the same line with the y increased by 5
Which system of linear equations can be solved using the information below?-314.1--2014-1-22 208-192|Ax| ==
Given
[tex]\begin{gathered} |A_x|=det\begin{bmatrix}{20} & {-3} \\ {-192} & {8}\end{bmatrix} \\ |A_y|=det\begin{bmatrix}{2} & {20} \\ {12} & {-192}\end{bmatrix} \end{gathered}[/tex]To find:
The system of equation.
Explanation:
It is given that,
[tex]\begin{gathered} |A_x|=det\begin{bmatrix}{20} & {-3} \\ {-192} & {8}\end{bmatrix} \\ |A_y|=det\begin{bmatrix}{2} & {20} \\ {12} & {-192}\end{bmatrix} \end{gathered}[/tex]That implies,
Since,
[tex]\begin{gathered} |A_x|=det\begin{bmatrix}{20} & {-3} \\ {-192} & {8}\end{bmatrix} \\ |A_y|=det\begin{bmatrix}{2} & {20} \\ {12} & {-192}\end{bmatrix} \end{gathered}[/tex]Then,
[tex]AX=B\Rightarrow\begin{bmatrix}{2} & {-3} \\ {12} & {8}\end{bmatrix}\begin{bmatrix}{x} & {} \\ {y} & {}\end{bmatrix}=\begin{bmatrix}{20} & {} \\ {-192} & \end{bmatrix}[/tex]Therefore,
The system of equation is,
[tex]\begin{gathered} 2x-3y=20 \\ 12x+8y=-192 \end{gathered}[/tex]Hence, the answer is option A).
After a party, Ronen noticed that of a pound of treats remained. He decided to take six tenths, or 0.6 of that amount to school and keep the rest of himself. What fraction of the remaining treats will Ronen bring to school? Drag and Drop the numerical values to make the fraction. 4 15 1 20 27 7
Treats remain = 1 pound
amount bringed to school = 0.6 = 6/10 =3/5
Multiply the treats remain (1 pound )
6/10 X 1 = 3/5 x1 = 3/5
Humphrey measured the height of his fence at 6 feet 7 inches. How many inches tall is Humphrey's fence?
6 feet 7 inches
1 feet = 12 inches
6 feet = 6(12) = 72 inches
6 feet 7 inches = 72 + 7 = 79 inches
Answer:
79 inches
A dietitian believes that eating more leafy green vegetables lowers blood pressure. She asks a group of you and yourfriends to continue eating as you normally do. She asks your brother and his friends to add two servings of spinach totheir daily diet. She records the blood pressure levels of all subjects before and after the diet change. Which group of anexperiment are you part of?-single-blind-confounding-control-experimental
In this experiment, the following points are to be noted:
1) you and your friends are to continue with the normal meal they usually take
2) your brother and his friends are to add two servings of spinach to their daily meals.
From these two points mentioned, the dietician did not care about the normal meals that the participants always ate even before the experiment.
Also, all other factors that affect blood pressure apart from food are not considered. The participants are not subjected to the same conditions.
We can then conclude that the experiment is not controlled.
Since both the experimenter (the dietician in this case) and the participants know about the make up of the test, it is not a single-blind test.
Since all the possible variables that affect body pressure are not made identical for all the participants, the experiment is a confounding experiments
Interpret f(10)F(x)= 0.08x^3+x^2+x+0.26
The Solution:
Given the function:
[tex]f(x)=0.08x^3+x^2+x+0.26[/tex]We are asked to find and interpret f(10).
[tex]f(10)=0.08(10^3)+(10^2)+(10)+0.26[/tex][tex]\begin{gathered} f(10)=0.08(1000)+100+10+0.26=80+100+10+0.26 \\ f(10)=190.26 \end{gathered}[/tex]Therefore, the correct answer is 190.26
This means when x=10, f(10)=190.26
A polygon has an area of 80 square units what scale factor would be required to dilate the polygon to five square units
The polygon has an area of 80 square units.
We need to find the scale factor to dilate it to 5 square units.
We need to that "The ratio of the area of one figure to the area of another, similar figure is equal to the square of the scale factor between the two figures"
Then:
The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 13 minutes.What is the probability that washing dishes tonight will take me between 9 and 10 minutes?Give your answer accurate to two decimal places.
Okay, here we have this:
Considering the provided information we obtain that:
-The interval duration between 8 minutes and 13 minutes is 5 minutes. And the interval duration between 9 and 10 minutes is 1 minute. So, we have that the probability in this case is the ratio of the duration intervals: 1/5=0.20=20%.
Finally we obtain that the probability that washing dishes tonight will take him between 9 and 10 minutes is 20%.
What is the value of z in the equation 2(4z − 6 − 6) = 170 − 46? 12.515.516.518.5
Explanation
give
[tex]2(4z-6-6)=170-46[/tex]Step 1
a) do the operations inside the parenthesis and do the subtraction in the rigth side
[tex]\begin{gathered} 2(4z-6-6)=170-46 \\ 2(4z-12)=124 \\ \end{gathered}[/tex]b) apply the distributive property to break the parenthesis
[tex]\begin{gathered} 2(4z-12)=124 \\ 8z-24=124 \end{gathered}[/tex]c) add 24 in both sides
[tex]\begin{gathered} 8z-24=124 \\ 8z-24+24=124+24 \\ 8z=148 \end{gathered}[/tex]d) finally, divide both sides by 8
[tex]\begin{gathered} 8z=148 \\ \frac{8z}{8}=\frac{148}{8} \\ z=18.5 \end{gathered}[/tex]therefore, the answer is
18.5
I hope
Need help asap I need to get this question right
The given expression is:
[tex](x-2)(x+4)[/tex]It is required to simplify the product using the distributive property.
Apply the distributive property to the product:
[tex](x-2)(x+4)=x(x+4)-2(x+4)[/tex]Apply the distributive property again to simplify the expression on the right:
[tex]\begin{gathered} x(x+4)-2(x+4)=x\cdot x+x\cdot4+(-2)\cdot x+(-2)\cdot4 \\ =x^2+4x-2x-8 \\ =x^2+2x-8 \end{gathered}[/tex]The answer is x²+2x-8.
Robert is told the size of angle BAC in degrees and he is then asked to calculate
the length of the line BC. He uses his calculator but forgets that his calculator
is in radian mode. Luckily he still manages to obtain the correct answer. Given
that angle BAC is between 10° and 15°, use graphing software to help you find
the size of angle BAC, correct to 2 decimal places.
The measure of angle BAC is of 14.48º, considering the relations in a right triangle.
What are the relations in a right triangle?There are three relations in a right triangle, presented as follows:
The sine of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is represented by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Using a ruler, it is found that the length of the opposite side to angle BAC, of CB, is of 1.5 cm, hence the following relation is established, considering the hypotenuse of 6 cm.
sin(x) = 1.5/6
In which x is the measure of angle BAC.
x can be isolated applying the arc sine function, which is the inverse of the sine, hence:
x = arcsin(1.5/6)
x = 14.48º.
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if the premium for same day shipping is 200%. what is the cost to ship 2000 lbs of goods from Houston to Shreveport (240 miles) using same-day shipping?
Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given distance
[tex]\begin{gathered} Distance=240\text{ miles} \\ premium=200\% \\ cost=2000lbs \\ price\text{ per 100 lbs for 240 miles is \$120} \end{gathered}[/tex]STEP 2: Calculate the cost
[tex]\begin{gathered} 100lbs\text{ for 240 miles = \$}120 \\ 2000=x \\ \\ x=\frac{2000\cdot120}{100}=\text{ \$}2400 \end{gathered}[/tex]STEP 3: Calculate the premium
[tex]200\%=\frac{200}{100}\cdot2400=\text{ \$}4800[/tex]STEP 4: Calculate the overall cost to ship required goods
[tex]\text{ \$}2400+\text{ \$}4800=\text{ \$}7200[/tex]Hence, the cost to ship 2000 lbs of goods from Houston to Shreveport (240 miles) using same-day shipping is $7200
find the values of X and Y in the image below and then find the measures of the four angles in the trapezoid
Answer:
x = 45, y = 115; 90, 90, 115, 65
Explanation:
One of the properties of a trapezoid is that adjacent angles of the legs of the trapezoid are supplementary, that is, they add up to 180 degrees.
Considering the above property, we'll have;
[tex]\begin{gathered} y+(y-50)=180 \\ 2y-50=180 \\ 2y=180+50 \\ y=\frac{130}{2} \\ y=115^{\circ} \end{gathered}[/tex]Still considering the above property, we have;
[tex]\begin{gathered} 2x+90=180 \\ 2x=180-90 \\ x=\frac{90}{2} \\ x=45 \end{gathered}[/tex]We can see that the measure of the four angles of the trapezoid are;
[tex]\begin{gathered} 2x=2(45)=90^{\circ} \\ \text{Right angle = 90}^{\circ} \\ y=115^{\circ} \\ (y-50)=115-50=65^{\circ} \end{gathered}[/tex]The following figures all have the same height and same base area. B В sa For which of the figures can we apply Cavalieri's principle to show they have the same volume? Choose 1 answer: A Only A and B Only A and C Only B and C A, B. and C
Cavalieri's principle states that if two figures have the same height and the same cross-sectional area at every point along with that height, they have the same volume.
Then, we can apply Cavalieri's principle to show A and B have the same volume.