The number of students attending the field trip is 304 and the number of adults is 114.
Calculating number of students and adults attending a field tripFrom the question, we are to determine the number of students and adults attending the field trip.
From the given information,
"The ratio of the number of adults to the number of students at a field trip has to be 3:8"
Let the number of students be x and the number of adults be y
Thus,
y/x = 3/8
8y = 3x ------------- (1)
Also,
There are 190 more students on the trip than there are adults
That is,
x - y = 190
Therefore,
x = 190 + y -------------- (2)
Substitute into equation
8y = 3x
8y = 3(190 + y)
8y = 570 + 3y
8y - 3y = 570
5y = 570
y = 570/5
y = 114
Thus, the number of adults is 114
Substitute the value of y into equation (2)
x = 190 + y
x = 190 + 114
x = 304
Hence, the number of students is 304
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Show that (fof-1) (x)=x and (F-1 of)(x) = x for the following pair of functions.f(x) = 5-4x, f'(x) =5-754Show that (fof-1)(x) = x.(fof- ')(x) = 0Write the expression for the composition.= x(Do not simplify. Type an exact answer, using radicals as needed.)
To obtain the expression for the composition of the function of the inverse function of x, the following steps are necessary:
Step 1: Write out the expression for the function of x and the inverse function of x, as below:
[tex]\begin{gathered} f(x)=\sqrt[5]{5-4x} \\ ^{}f^{-1}(x)=\frac{5-x^5}{4} \end{gathered}[/tex]Step 2: Write out the expression for the composition of the function of the inverse function of x, as below:
[tex](f^{-1}Of))(x)=^{}\frac{5-(\sqrt[5]{5-4x})^5}{4}[/tex]Thus, the above is how the expression for the composition of the function of the inverse function of x is to be written out
Simplify the expression 8h + (-7.3d) - 14 + 5d - 3.2h
The expression is:
8h + (-7.3d) - 14 + 5d - 3.2h
collecting like terms, we have:
8h - 3.2h +(-7.3d) + 5d - 14
= 4.8h - 7.3d + 5d - 14
= 4.8h - 2.3d - 14
That is the expression simplified
7. Simplify28120.51 +423) + (222 +7.51).
Answer: 581.5i + 140.64
Explanation:
574i + 118.44 + 22.2 +7.5i
grouping the terms yield
574i + 7.5i + 118.44 + 22.2
⇒
You Try! As an Equation Example B: A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet. Find the dimensions of the rectangle. Write an equation to model this problem and solve it in the sketch area below. 市里。 Entrega
Let the width be w and the length be l
Since the width is 5ft less than the length,
then
w=l-5
The area of the rectangle is 126 square feet
Then
l times w = 126
therefore
l(l-5) = 126
[tex]\begin{gathered} \Rightarrow l^2-5l=126 \\ \Rightarrow l^2-5l-126=0 \end{gathered}[/tex]Factorising the equation, we have:
[tex]\begin{gathered} l^2+9l-14l-126=0 \\ \Rightarrow(l+9)(l-14)=0 \\ \Rightarrow l=-9\text{ or 14} \end{gathered}[/tex]Since l cannot be negative
then the only correct option is l=14
Since w = l - 5
then
w = 14 - 5 = 9
Therefore the length is 14ft and the width is 9ft
PLEASE HELP ME !!!!!!!!
Find and describe the error in the following problem
Answer:
When multiplying the bottom equation, they did not multiply 4y by -2, but instead by 2.
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The domain is the set of all possible inputs that would satify the function while the range is the set of possible output values
Looking at the given graph,
Domain = ( - infinity, 4)
Range = (- 5, 2)
The half-life of a certain substance is 27 years. How long will it take for a sample of this substance to decay to 66% of its original amount? for the sample of the substance to decay to 66% of its original amount
This is a type of radioactive decay problem. Given an initial amount of N0, the amount at t years is given by
[tex]N(t)=N_0e^{-\lambda t}[/tex]The information "27 years is the half-life of the substance" means that if we replace t by 27, we will get exactly half of the initial amount we had. That is
[tex]N_0e^{-\lambda\cdot27}=\frac{N_0}{2}[/tex]We can cancell out N0 on both sides, so we get
[tex]e^{-\lambda\cdot27}=\frac{1}{2}[/tex]using the properties of exponentials, we have the equivalent equation
[tex]\frac{1}{2}=\frac{1}{e^{\lambda\cdot27}}[/tex]which is also equivalent to
[tex]e^{\lambda\cdot27}=2[/tex]If we apply natural logarithm on both sides, we get
[tex]\ln (e^{\lambda\cdot27})=\lambda\cdot27=\ln (2)[/tex]Finally, we can divide both sides by 27, to get
[tex]\lambda=\frac{\ln (2)}{27}[/tex]So, the function that describes the amount of the subtances at time t is given as
[tex]N(t)=N_0e^{\frac{-\ln (2)\cdot t}{27}}[/tex]Now, we want to calculate the value of t, for which the amount we have at year t is exactly 66% of what we have at t=0. That is
[tex]\frac{N_0e^{-\frac{\ln (2)\cdot t}{27}}}{N_0}=0.66[/tex]We can cancell out N0 and, by equivalence by using the properties of exponents, we get
[tex]\frac{1}{e^{\frac{\ln(2)}{27}\cdot t}}=0.66[/tex]which is also equivalent to
[tex]\frac{1}{0.66}=e^{\frac{\ln (2)t}{27}}[/tex]if we apply the natural logarithm on both sides, we get
[tex]\ln (\frac{1}{0.66})=\ln (e^{\frac{\ln(2)\cdot t}{27}})=\ln (2)\cdot\frac{t}{27}[/tex]Finally, we want to solve for t. To do so, we can multiply by 27 and then divide by ln(2). So we get
[tex]t=\frac{27}{\ln(2)}\cdot\ln (\frac{1}{0.66})[/tex]with help of a calculator, we have that t is approximately 16.185. That is, about after 16 years, we will have 66% of the initial amount.
uueJUU Telp Find the area of the polygon. The area of the polygon is (Type a whole number.) 4 cm 7 cm 7 cm -14 cm 14 cm יד 4 cm
The area of the polygon = Sum of area of eight triangles + area of a square.
Area of the square
[tex]\begin{gathered} \\ \text{Length = 14cm} \\ \text{Area of the square = Length}^2 \\ \text{ = 14}^2 \\ =196cm^2 \end{gathered}[/tex]Area of one triangle
[tex]\begin{gathered} =\text{ }\frac{Base\text{ x Height}}{2} \\ \text{Base = 4cm} \\ \text{Height = 7cm} \\ =\text{ }\frac{4\text{ x 7}}{2} \\ =\text{ }\frac{28}{2} \\ =14cm^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the eight triangles = 8 x 14 } \\ \text{ = 112 cm}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the polygon = 196 + 112} \\ \text{ = 308 cm}^2 \end{gathered}[/tex]5. * 20 points Rotate 180° about the origin. 3 Y 4 5 3
In order to rotate these point 180° about the origin, we just need to change the signal of all coordinates.
So we have that:
[tex]\begin{gathered} X(-1,3)\to X^{\prime}(1,-3) \\ W(-2,5)\to W^{\prime}(2,-5) \\ V(-5,5)\to V^{\prime}(5,-5) \\ T(-4,3)\to T^{\prime}(4,-3) \end{gathered}[/tex]Looking at the options, the correct one is c. (the third one).
fill in the blanks.30x8=3x_____x840x7=_____x10x7
Answer:
30x8=3x_10_x8
40x7=_4_x10x7
First one: 10
Second one: 4
12. One year ago the median price for a home was $342,000. Now the current median price for a home is $215,000. What was the percent decrease in the median price of a home over the last year? Give your answer to at least one decimal place.%
One year ago the median price for a home was $342,000. Now the current median price for a home is $215,000. What was the percent decrease in the median price of a home over the last year? Give your answer to at least one decimal place.
In this problem
$342,000 ------> represents 100%
so
Applying proportion
Find out how much percentage represents the difference (342,000-215,000=127,000)
100/342,000=x/127,000
solve for x
x=(100/342,000)*127,000
x=37.1%The table summarizes results from 977 pedestrian deaths that were caused by automobile accidents.Pedestrian DeathsDriverPedestrian Intoxicated?Intoxicated?YesNoYes4885No260584If one of the pedestrian deaths is randomly selected, find the probability that neither the pedestrian nor the driver wasintoxicated. Please enter a decimal to 4 places.Probability
We are asked to find the probability that neither the pedestrian nor the driver was intoxicated.
Probability is given by
P = number of desired outcomes/total number of outcomes
From the given table we know that
Total number of pedestrian deaths = 977
The desired outcomes are
Driver intoxicated = No and Pedestrian intoxicated = No (584)
So the probability is
P = 584/977
P = 0.5977
Therefore, the probability that neither the pedestrian nor the driver was intoxicated is 0.5977
Mr. Cumme bought the amount of clay listed for his class.- 2.2 kilograms- 1.5 kilograms- 850 grams - 700 gramshow many grams of clay did Mr.Cumme buy?
Hello there. To solve this question, we have to remember how to convert kilograms to grams.
Given an amount in kilograms, to determine its value in grams, we simply multiply it by 1000.
In this case, we know that Mr. Cume bought the amount of clay listed for his class:
- 2.2 kilograms
- 1.5 kilograms
- 850 grams
- 700 grams
To determine how many grams of clay he bought, we start converting the values from kilograms to grams
2.2 kilograms * 1000 = 2200 grams and
1.5 kilograms * 1000 = 1500 grams
Now, we add everything
2200 + 1500 + 850 + 700 = 5250 grams
This is the final answer to this question.
Vihaan got 38/48 on his geography test. Sahaj got 80% on his geography test. Jada got 0.8125 on her geography test. Quinn thinks that Vihaan got a higher mark on his test than Sahaj and Jada.Is Quinn right? Prove whether he is right or wrong by showing your work (5 marks)
Vihaan got 38 in her geography test
Since the geography test has a total score of 48
Since Sahaj got 80% of it, then multiply 80/100 by 48 to find his score
[tex]\frac{80}{100}\times48=38.4[/tex]Sahaj got 38.4 on the geography test
Since Jada got 0.8125 on her geography test, then multiply 0.8125 by 48 to find her score
[tex]0.8125\times48=39[/tex]Jada got 39 on the geography test
The greatest one is Jada, then Sahaj, then Vihaan
Quinn thinks that Vihaan got the higher score
But Jada the one who got the higher score
Then Quinn is not right
A credit union client deposits $2,700 in an account earning 6% interest, compounded annually. What will the balance of the account be at the end of 31 years?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Balance ≈ $________ after 31 years.
Answer:
Balance ≈ $7,722 after 31 years
Step-by-step explanation:
multiply your deposit by your interestMultiply by how longAdd your base deposit to the interestEx.
2, 700(0.06) =$162.
162(31)= $5,022.
5,022 + 2,700 = $7,722.
If 3 girls can decorate 2 holiday cards in 1.5 minutes, how many holiday cards can 6 girls decorate in 1 hour if they work at the same speed?
Notice that 2*3=6.
On the other hand, according to the question, 3 girls can decorate a total of
[tex]\begin{gathered} \frac{60}{1.5}=40 \\ \Rightarrow40\cdot2=80 \end{gathered}[/tex]80 holiday cards in one hour. Therefore, 6 girls can decorate 2*80=160 holiday cards in the same amount of time.
The answer is 160 holiday cards per hour
Convert 15% to a fraction. Write in lowest terms.Convert 26% to a fraction. Write in lowest terms.Read the "Fractions, Decimals & Percents" lesson. Then answer each of the following questions to practice converting between fractions, decimals and percents.
Convert 15% to a fraction. Write in the lowest terms.
So,
[tex]15\%=\frac{15}{100}=\frac{5\times3}{5\times20}=\frac{3}{20}[/tex]So, the answer will be 15% = 3/20
=========================================================
Convert 26% to a fraction. Write in the lowest terms.
So,
[tex]\frac{26}{100}=\frac{2\times13}{2\times50}=\frac{13}{50}[/tex]So, the answer will be 26% = 13/50
can you please solve this problem then tell me what was wrong with the answer
Given:
[tex]64^{\circ\text{ }}and\text{ }x^{\circ}[/tex]Sum of the angles of Same side interior angles is 180 degree.
[tex]\begin{gathered} 64+x=180 \\ x=180-64 \\ x=116^{\circ} \end{gathered}[/tex]what do factors 12 and 24 have in common
Mcd (max common divisor) of 12, 24 = 12
(Because 24/12= 2 )
are
2,3,4,6,12
radical 9 cubed times radical -24 cubed=?
we can easily calculate that -6 times -6 times- 6 =- 216 it is why we can do this equality
because we have an exponent 3 and a cubic root we can cancel both so the answer of
[tex]\sqrt[3]{9}\text{ }\cdot\sqrt[3]{-24}=\text{ -6}[/tex]Charlotte is making pies for her whole family. So far, she has made 5.04 pounds
worth of pie, and has 7 people to feed, including herself. How much does each
person get if Charlotte is finished making pies?
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more
people to feed, how much pie will each person get from Charlotte's 5.04
pounds?
Step-by-step explanation:
Charlotte is making pies for her whole family. So far, she has made 5.04 pounds worth of pie, and has 7 people to feed, including herself. How much does each person get if Charlotte is finished making pies?
5.04 / 7 = 0.72 pounds per person
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more people to feed, how much pie will each person get from Charlotte's 5.04 pounds?
7 + 2 = 9 people now
5.04 / 9 = 0.56 pounds per person
-4x-2y = -6a. y = -2x + 3b. y = 2x-3C. y = 2x + 3d. y = -2x - 3
Can you please help me out with a question
The volume of the figure = volume of first cone + volume of second cone + volume of a hemisphere
Formula
Volume of a cone = 1/3πr²h
The volume of hemisphere = 2/3πr³
Therefore
r = radius , h = height
where h1 = 20in , h2 = 18in and r = 15in
Volume of the first cone = 1/3πr²h1
= 1/3 x π x (15)² x 20
= 1500π in³
Volume of the second cone = 1/3πr²h2
= 1/3 x π x (15)² x 18
= 1350π in³
Volume of hemisphere = 2/3πr³
= 2/3 x π x (15)³
= 2250π in³
Therefore
The volume of the figure = 1500π in³ + 1350π in³ + 2250π in³
= 5100π in³
Hence the volume of the figure = 5100π in³
Tracey paid $145 for an item that was originally priced at $550. What percent of the original price did Tracey pay?
Tracey paid $145 for an item that was originally priced at $550. What percent of the original price did Tracey pay?
we know that
$550 represent 100%
so
Applying proportion
100/550=x/145
solve for x
x=(100/550)*145
x=26.36%Use an alternative method to express the following set: {y:y is a person in your math class and also more than 100 years old.}
Let's use the letter M to label the math class. The fact that person y is in that class can be expressed by:
[tex]y\in M[/tex]We also have to show that is older than 100 so we have:
[tex]y>100[/tex]If we put all this information together we get:
[tex]\mleft\lbrace y\colon y\in M,y>100\mright\rbrace[/tex]And that's an alternative way to express the set.
i need help with this problem Find rate of change.
Step 1:
First, pick two points where the line intercept with both the horizontal and the vertical axis.
( 0 , 300 ) and (
9. Alberta Emery can sew a dress in 3 days. Allison Taylor requires only 2 days. If theycombine efforts to fill one order to sew 30 dresses, how long will they take to fill the order?Answer
Given that Alberta Emery can sew 1 dress in 3 days. so the efficiency of Alverta Emery is given by,
[tex]=\frac{1}{3}\text{ work per day}[/tex]Similarly, given that Allison Taylor takes 2 days to sew 1 dress, so the efficiency of Allison Taylor is given by,
[tex]=\frac{1}{2}\text{ work per day}[/tex]When they combine their efforts, the amount of work done per day is given by,
[tex]\begin{gathered} =\frac{1}{3}+\frac{1}{2} \\ =\frac{2+3}{6} \\ =\frac{5}{6}\text{ work per day} \end{gathered}[/tex]So the number of days required to sew 30 dresses when both of them work together, is calculated as,
[tex]\begin{gathered} =\frac{30}{\frac{5}{6}} \\ =30\cdot\frac{6}{5} \\ =6\cdot6 \\ =36 \end{gathered}[/tex]Thus, they will take 36 days to sew 30 dresses.
The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 69?
Given:
The box-and-whisker plot below represents some data set.
As shown:
The median = 65
The value of Q1 = 61
The value of Q3 = 69
The percentage of the data values that are greater than 69 will be the percentage of the data that are greater than Q3
So, the answer will be 25%
What are lim f(x) and lim f(x) if they exist?
SOLUTION:
Case: Limits
Method:
Right and left-sided limits.
The right sided limits is gotten from the right-hand side and gives an f(x) of 0 while the left sided limits gives an f(x) of 1.
Final answer: Option
[tex]\begin{gathered} \lim_{x\to0^-}f(x)=1 \\ \lim_{x\to0^+}f(x)=0 \end{gathered}[/tex]Susan monitors the number of strep infections reported in a certain neighborhood in a given week.The recent numbers are shown in this table:WeekNumber of People020126234344According to her reports, the reported infections are growing at a rate of 30%.If the number of infections continues to grow exponentially, what will the number of infections bein week 10?
SOLUTION
The formula for growth rate is given below;
[tex]y=a(1+r)^x[/tex]Where;
y = number of infections,
a = initial number of infections (20),
r = rate (30% or 0.3) and
x = the week to find (10)
[tex]\begin{gathered} y=a(1+r)^x \\ y=20(1+0.3)^{10} \\ y\text{ = 20 (13.7858)} \\ y\text{ = 275.72} \end{gathered}[/tex]The number of infections in week 10 will be 276.