We know that
• There are 13 students in group A.
,• 25% of the class is in group A.
,• 75% of the class is in group B.
Based on the given information, 13 students represent 25% of the class, which is group A. To find the numbers of students in group B, we can form the following proportion.
[tex]\frac{13}{0.25}=\frac{x}{0.75}[/tex]Then, we solve for x.
[tex]\begin{gathered} x=\frac{13\cdot0.75}{0.25} \\ x=39 \end{gathered}[/tex]Hence, there are 39 students in group B.A farmer looks over a field and sees 36 heads and 102 feet. Some are pigs, some are geese. How many of each animal are there?
There are:
36 heads and 102 feet.
The total number of animals (pigs+geese) are 36, also we know that the pigs have 4 feet and the geese 2.
Therefore, the equations to find it will be:
1. For the heads:
[tex]36=p+g\text{ \lparen1\rparen}[/tex]For the feet:
[tex]102=(4*p+2*g)\text{ \lparen2\rparen}[/tex]Where p=pigs and g= geese.
Solving the equations using substitution method:
Isolating p in (1):
[tex]36-g=p\text{ \lparen3\rparen}[/tex]Substituing (3) in (2):
[tex]\begin{gathered} 102=4p+2g \\ 102=4(36-g)+2g \end{gathered}[/tex]Solving for g:
[tex]\begin{gathered} 102=144-4g+2g \\ 102-144=-2g \\ -42=-2g \\ g=\frac{42}{2}=21 \end{gathered}[/tex]Finally, putting g=21 in (3):
[tex]\begin{gathered} p=36-g \\ p=36-21=15 \end{gathered}[/tex]Answer: There are 15 pigs and 21 geese.
You want to express this number in scientific notation.437,000What is the first step?Move the decimal point 5 places to the right to get 4.37.Move the decimal point 5 places to the left to get 4.37.Move the decimal point 4 places to the left to get 4.37.O Move the decimal point 4 places to the right to get 4.37.
To express the number:
437000
You need to move the decimal point 5 places to the left to get 4.37. That is:
If the probability of an event is 62%, what is the probability of its complement?
Complement of probability, what is the meaning of it?
It is all the outcomes not in the event
The total of probability is 100%
62% of them are in the event
Then the complement is the rest
100% - 62% = 38%
The probabilty of its complement is 38%
where is the graph increasing?where is the end behavior on the graph?where is the graph decreasing?
Solution
For this case the function is increasing on the intervals:
(-2.5, 0) and (3, infinity)
the end behavior is
[tex]x\rightarrow\infty,f(x)\rightarrow\infty[/tex]The graph is decreasing in the following intervals:
(-infinity, -2.5) and (0,3)
Question 11 ptsConsider the inequality -15%A. Predict which values of x will make the inequality true and write your prediction inthe box.B. Create the table in your scratch paper to check your prediction. Were you correct?Why or why not?-4-3-2-101234
Solve the inequality for x
[tex]\text{ x }\ge\text{ -2}[/tex]Values of x that will the inequality true are -1, 0, 1 , 2, 3, 4, etc
b)
[tex]\text{ }\frac{-4}{2}\text{ = -2 }\ge\text{ -1 false}[/tex][tex]\text{ }\frac{-3}{2}\text{ }\ge\text{ -1 false }[/tex][tex]\text{ }\frac{-2}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{-1}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{0}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{1}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{2}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{3}{2}\text{ }\ge\text{ -1 true}[/tex][tex]\text{ }\frac{4}{2}\text{ }\ge\text{ -1 true}[/tex]
i don’t understand what the term one to one means
From the given functions, let's select the functions that are one-to-one functions.
A function is said to be a one-to-one function when it produces different outputs for different inputs (values of x).
The easiest way to determine if a function is a one-to-one function is to graph the function and use the horizontal line test.
Now, let's check the functions to determine.
• Function 1.
f(x) = x³ - 7
Since the leading exponent is an odd number, this function can be said to be a one-to-one function.
• Function 2.
f(x) = x² - 4
The leading exponent of this function is an even number. Since it is even, it will fail the horizontal line test. Therefore, the function is NOT a one-to-one function.
• Function 3.
[tex]f(x)=\frac{1}{8x-1}[/tex]This function is a one-to-one function.
• Function 4.
[tex]f(x)=\frac{5}{x^4}[/tex]This function is a one-to-one function.
• Function 5.
f(x) = |x|
This function is NOT a one-to-one function since it will fail the horizontal line test.
Therefore, the functions that are one-to-one are:
[tex]\begin{gathered} f(x)=x^3-7 \\ \\ f(x)=\frac{1}{8x-1} \\ \\ f(x)=\frac{5}{x^4} \end{gathered}[/tex]help the answers are CPCTC Definition of congruence SAS and SSS
SOLUTION
From the question given the following statements to prove are correct, then the last part
[tex]\Delta RSU\cong\Delta TSV[/tex]The reason is Side-side-side triangle theorem
This theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Hence the answer is Side-side-side triangle theorem
A square has an area of 50 square cm. Which of the following best describes the square's perimeter? 1 O 12 O 14 cm 12 cm O 25 cm O 28 cm
The area of square goes by the formula:
[tex]A=s^2[/tex]Where
A is the Area
s is the side length
Given,
A = 50, the side length is:
[tex]\begin{gathered} A=s^2 \\ 50=s^2 \\ s=\sqrt[]{50} \\ s=5\sqrt[]{2} \end{gathered}[/tex]We want the perimeter of the square, which is:
[tex]P=4s[/tex]Where
P is perimeter
s is side length
So,
[tex]\begin{gathered} P=4s \\ P=4(5\sqrt[]{2}) \\ P=20\sqrt[]{2} \\ P=28.28 \end{gathered}[/tex]Rounded to nearest whole number: 28 cm
I'm trying to find the probability of a spinner landing on the letter A Wendy spinner contains three A's one B two C and one D how many desired outcome are there
Probability is expressed as
number of desired outcomes/number of total outcomes
Given that the spinner contains three A's one B two C and one D, the total outcomes are
A A A B C C D
If the desired outome is the probability of a spinner landing on the letter A, then the number of desired outcomes is the number of A which is 3
The correct answer is 3
you were given a rectangle with dimension of length equals 60 inches and width equals 4J the perimeter of the rectangle is 400 in what is the value of j
Given data:
The given length of the rectangle is L=60 inches.
The given width of the rectangle is bB=4J.
The perimeter of the rectangle is P=400 inches.
The expression for the perimeter of the rectangle is,
P=2(L+B)
Substitute the given values in the above expression.
400 inches=2(60 inches+4J)
200 inches=60 inches+4J
140 inches=4J
J=35 inches
Thus, the value of J is 35 inches.
(A) how many cubic meters of sand can the sandbox hold? (B) the manufacture suggested the sandbox should be filled to 89% capacity. How many cubic meters of sand is this?
To solve this problem, we must find the volume of the sandbox.
[tex]V=l\cdot w\cdot d[/tex]Where:
[tex]\begin{gathered} l=30m \\ w=26m \\ d=4m \end{gathered}[/tex]Now, we replace and solve:
[tex]\begin{gathered} V=30m\cdot26m\cdot4m \\ V=3120m^3 \end{gathered}[/tex]The A answer is 3120 cubic meters
Now, for question "b" we must find how many cubic meters are 89% of its capacity, that is 89% of the capacity of the 3120 cubic meters.
For this, we multiply the total capacity of the sandbox by 0.89.
[tex]3120\cdot0.89=2776.8[/tex]The A answer is 2776.8 cubic meters
What is the measure of angle x for this ramp?
1) Let's find out the angle x, using trigonometric ratios. So since we have the opposite leg to angle x and the adjacent leg to angle x we can write out that:
[tex]\sin (X)=\frac{1}{12}[/tex]2) But since we want to know the angle, so we need to calculate the arcsine of (x):
[tex]undefined[/tex]A box contains 5 balls. Two are numbered 3, one is numbered 4,and two are numbered 5. The balls are mixed and one is selected at random. After a ball is selected,it’s number is recorded. Then it is replaced. If the experiment is repeated many times. Find the variance and standard deviation of the numbers on the balls.
Solution:
Let X be the number on each ball. The probability distribution is:
now, the mean is
[tex]\mu=\sum_^X\text{ . P\lparen X})[/tex]According to the data, this Mean would be:
[tex]\mu=\sum_^X\text{ . P\lparen X})\text{ }=\text{ 3 . }\frac{2}{5}\text{ }+4\text{ . }\frac{1}{5}\text{ }+5\text{ . }\frac{2}{5}\text{ }=4[/tex]So, we get that the Mean is:
[tex]\mu=4[/tex]Now, the variance is
[tex]\sigma\text{ }=\text{ }\sum_^\lbrack X^2\text{ . P\lparen X})\rbrack-\mu^2[/tex]According to the data of the problem, we get that the variance is:
[tex]\sigma=\text{ }\lbrack\text{3}^2\text{ . }\frac{2}{5}\text{ }+4^2\text{ . }\frac{1}{5}\text{ }+5^2\text{ . }\frac{2}{5}\text{ }\rbrack\frac{}{}-4^2[/tex]this is equivalent to:
[tex]\sigma=\frac{4}{5}[/tex]Thus, the standard deviation would be:
[tex]\sqrt{\frac{4}{5}}=0.894[/tex]Then, we can conclude that the correct answer is:
Variance:
[tex]\frac{4}{5}[/tex]Standard deviation:
[tex]0.894[/tex]A box of light bulbs is shipped to a hardware store. When it arrives, 4 of the bulbs are broken. Predict the number of broken light bulbs in an order of 125 bulbs.
As 4 of 25 light bulbs are broken you use a rule of three to find the number of broken bulbs in a order of 125:
[tex]x=\frac{125\cdot4}{25}=\frac{500}{25}=20[/tex]Then, in a order of 125 bulbs the prediction is 20 broken bulbsMy ex represented in the public will buy for an object and P represent the object unit three suppose that the universe
we have the linear equation
[tex]p=(-\frac{1}{5})x+200[/tex]Part A
the Revenue is equal to
R(x)=p*x
substitute
[tex]R(x)=\lbrack(-\frac{1}{5})x+200\rbrack\cdot x[/tex][tex]R(x)=-\frac{1}{5}x^2+200x[/tex]Part B
the function of revenue is a quadratic equation (vertical parabola opens downward)
the vertex represents a maximum
using a graphing tool
see the attached figure
the vertex is the point (500, 50000)
therefore
the value of x that maximizes the revenue is
x=500
Part C
For x=500
Find out the unit price
[tex]\begin{gathered} p=(-\frac{1}{5})(500)+200 \\ p=100 \end{gathered}[/tex]the unit price is p=$100
Part D
the maximum revenue is the y-coordinate of the vertex
the vertex is (500, 50,000)
therefore
the maximum revenue is $50,000
Michael wanted to make chocolate milk. He used proportional reasoning based on the table. If his glassonly holds 2.5 cups, how many tablespoons of chocolate syrup does he need?
First, we find the ratio between the cups of mils and the tablespoons of chocolate syrup
[tex]\frac{6}{4}=1.5[/tex]The ratio is 1.5, which means we have to multiply this ratio by 2.5 cups.
[tex]2.5\times1.5=3.75[/tex]So, Michael needs 3.75 tablespoons of chocolate syrup to its 2.5 cups glass.
When Paisley moved into a new house, she planted two trees in her backyard. At thetime of planting, Thee A was 21 inches tall and Tree B was 33 inches tall. Each yearthereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. LetA represent the height of Tree At years after being planted and let B represent theheight of Tree Bt years after being planted. Write an equation for each situation, interms oft, and determine the interval of time, t, when Tree A is taller than Tree B.A= 21 + 6t – 6B = 33 + 3t-3Tree A is taller than Tree B whentNote: The interval will only apply for valid values oft in the domainSubmit Answer
Tree A
[tex]A=21+6t[/tex]Tree B
[tex]B=33+3t[/tex]To determine the interval, we must write that A is greater than B with an inequality
[tex]A>B[/tex]OR
[tex]21+6t>33+3t[/tex]and solve t
[tex]\begin{gathered} 6t-3t>33-21 \\ 3t>12 \\ t>\frac{12}{3} \\ t>4 \end{gathered}[/tex]so, the interval is
[tex](4,\infty)[/tex]It takes Maggie 12 minutes to walk to school. How many hours does it take to walk to school and back? ( 5 school days per week)
Maggie spends 12 minutes per trip, in one day she makes 2 trips and we are asked to calculate how many hours she spends on these trips in 5 days
First, we will do this calculation in minutes
[tex]12\cdot2\cdot5=120[/tex]She spends 120 minutes per week, now let's do the unit conversion, converting the minutes to hours, let's remember that one hour is the same as 60 minutes.
[tex]120\min \cdot\frac{1hr}{60\min }=2hr[/tex]The answer is 2 hours
Translate this phrase into an algebraic expression. Three less than the product of 12 and Victor's age Use the variable v to represent Victor's age.
Let V be Victor's age. Then, we can write:
[tex]12\cdot V-3[/tex]Calculate an estimate for the maximum number of drinks a 110lb female can consume without going over 0.08 BAC if she plans on leaving the party in 2 hours.
we have the following:
The formula is:
[tex]B=-0.015\cdot t+\frac{2.84\cdot N}{W\cdot g}[/tex]replacing,
where
B is blood alcohol content
t is the time
N is the maximum number of drinks
W is the weight
and g a gender constant (0.55 for wormen)
[tex]\begin{gathered} 0.08=-0.015\cdot2+\frac{2.84\cdot N}{110\cdot0.55} \\ \\ 0.08=-0.03+0.0469N \\ N=\frac{0.08+0.03}{0.0469} \\ N=2.34\cong2 \end{gathered}[/tex]therefor,e th
A bag contains 8 red balls and 3 blue balls. Two balls are drawn at random one after the other without replacement. Find the probability that the balls drawn are red.
First, we need to calculate the probability of drawing a red ball the first time. This is given by the usual probability:
[tex]P_{\text{red}1}=\frac{\text{red }}{total}=\frac{8}{11}[/tex]Now, as for the second time we pick a ball. Notice that the number of balls in the bag has changed since there is 1 red ball less. So, the probability of extracting a red ball under these conditions is:
[tex]P_{\text{red}2}=\frac{red}{\text{total}}=\frac{7}{10}[/tex]Notice that now the total number of balls is 10 and there are 7 red ones.
Finally, the probability we are looking for is given below:
[tex]P_{\text{red}1}\cdot P_{\text{red}2}=\frac{8}{11}\cdot\frac{7}{10}=\frac{56}{110}\approx0.50909\ldots\approx0.51[/tex]The probability is the above expression, in case you need it expressed as a fraction or a decimal number.
The top thing is question my answer is in the box am I correct and can you show me how to do it right if not
Formula
[tex]M=\frac{pm(1+m)^{na}}{(1+m)^{na}-1}[/tex]Given parameters
[tex]\begin{gathered} p=3,500 \\ m=\frac{8}{12\times100}=\frac{0.08}{12} \\ n=12\text{ } \\ a=2 \end{gathered}[/tex]Substitute the given parameters into the formula
[tex]M=\frac{3500(\frac{0.08}{12})(1+\frac{0.08}{12})^{24}}{(1+\frac{0.08}{12})^{24}-1}[/tex][tex]\begin{gathered} M=\frac{3500(\frac{0.08}{12})(1+\frac{0.08}{12})^{24}}{(1+\frac{0.08}{12})^{24}-1} \\ \\ \text{Remove the parent}heses\text{ (a)=a} \\ \frac{3500\cdot\frac{0.08}{12}\left(1+\frac{0.08}{12}\right)^{24}}{\left(1+\frac{0.08}{12}\right)^{24}-1} \\ \\ \text{Now} \\ \frac{3500\cdot\frac{0.08}{12}\mleft(\frac{0.08}{12}+1\mright)^{24}}{1.0066^{24}^{}-1} \\ \text{Multiply the numerator} \\ \frac{27.367}{1.00666^{24}-1} \\ \text{simplify} \\ =\frac{27.36738}{0.17288}=158.296 \\ \end{gathered}[/tex]The final answer
[tex]\text{ \$158.30}[/tex]simply the expression using rational exponents (4x^3)^1/2
The equation is given
[tex](4x^3)^{\frac{1}{2}}[/tex]Solving the expression,
[tex](2)^{\frac{1}{2}\times2}\times x^{\frac{3}{2}}=2x^{\frac{3}{2}}[/tex]The answer is
[tex]2x^{\frac{3}{2}}[/tex]Enter the correct answers in the boxes in the table.Evaluate each function in the table at f(3)
In order to complete the table it is only necessary to evaluate each function for x = 3.
To do this, replace by 3 where x is on each expression and solve the math operations, just as follow:
f(x) = 3x + 5
f(3) = 3(3) + 5 = 15 + 5 = 20
f(x) = 1/2 x² - 1.5
f(3) = 1/2 (3)² - 1.5 = 1/2 (9) - 1.5 = 3
f(x) = 3/(2x)
f(3) = 3/(2(3)) = 3/6 = 1/2 = 0.5
Hence, the numerical values to complete the table are 20, 3 and 0.5
Question 1 (1 point)If f(x) = 2x+7 and g(x) = -3x+5, what is f(g(1))?
ANSWER
f(g(1)) = 11
EXPLANATION
We are given that:
f(x) = 2x + 7
and
g(x) = -3x + 5
We want to find f(g(1)).
To do this, we have to find the value of g(x) when x = 1 and then put that value into f(x):
g(x = 1) = g(1) = -3(1) + 5
g(1) = -3 + 5
g(1) = 2
Now, put x = 2 in f(x):
f(g(1)) = f(x = 2) = f(2) = 2(2) + 7
f(g(1)) = 4 + 7
f(g(1)) = 11
Inverse of an exponential function fill in the chart. If needed, use a calculator and round to one decimal place.
ANSWER :
The answers from column to column are :
g, h and s
e, a and b
d, q and r
k, f and c
m, l and n
EXPLANATION :
From the problem, we have the function :
[tex]f(x)=e^x[/tex]The first column is the value of f(x) at given x values.
The second column is also the value of f(x) but written as a point (x, f(x))
The third column is the inverse of the function written as a point (f(x), x)
We will solve this from one column to another column.
That will be :
[tex]\begin{gathered} \text{ when x = 0} \\ f(0)=e^0=1 \\ (x,f(x))=(0,1) \\ (f(x),x)=(1,0) \\ \text{ The answers are g, h and s} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = 1} \\ f(1)=e^1\approx2.7 \\ (x,f(x))=(1,2.7) \\ (f(x),x)=(2.7,1) \\ \text{ The answers are e, a and b} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = -1} \\ f(-1)=e^{-1}\approx0.4 \\ (x,f(x))=(-1,0.4) \\ (f(x),x)=(0.4,-1) \\ \text{ The answers are d, q and r} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = 2} \\ f(2)=e^2\approx7.4 \\ (x,f(x))=(2,7.4) \\ (f(x),x)=(7.4,2) \\ \text{ The answers are k, f and c} \end{gathered}[/tex][tex]\begin{gathered} \text{ when x = -2} \\ f(-2)=e^{-2}\approx0.1 \\ (x,f(x))=(-2,0.1) \\ (f(x),x)=(0.1,-2) \\ \text{ The answers are m, l and n} \end{gathered}[/tex]g, h and s
Scatterplot help with problem C (8.5 million dollars,10.2million dollars,11.9million dollars,13.6million dollars, 15.3 million dollars)
ANSWER :
10.2 million dollars
EXPLANATION :
For C, we just need to locate the revenue of 50 million dollars and reflect it to the rental revenue.
It is around 10 million dollars.
From the choices, 10.2 million dollars is the closest.
Question 4The members of the high school swim team are in ratio of 4 boys to every 3 girls. Howmany boys are there if there are 15 girls on the team?on't knowOne attempt157wered 3 out of 3 correctly. Asking up to 9.204
hello
from the question given, we know the ratio between the boys to the girls are 4:3 and the number of girls are 15 on the team
[tex]b=\frac{15}{3}\times4=5\times4=20[/tex]the numbers of boys on the team are 20
Consider 0.3 x 0.1.How many digits after the decimal point will the product have?Numbers of digits =
In this case the number of digits after the decimal pointmust be 2 because each number has one digit after the decimal point.
Let X be a random variable with the following distribution. If E(X) = 108, then x2=
To obtain the value of x2, the following steps are necessary:
Step 1: Recall the formula for E(X) from probability theory, as follows:
From probability theory:
[tex]E(X)=\sum ^n_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2)+\cdots+X_n\cdot P(X_n)[/tex]Step 2: Apply the formula to the problem at hand to obtain the value pf x2, as follows:
[tex]\begin{gathered} \text{Given that:} \\ E(X)=108 \\ X_1=80,P(X_1)=0.3 \\ X_2=?,P(X_2)=0.7 \end{gathered}[/tex]We now apply the formula, as below:
[tex]\begin{gathered} E(X)=\sum ^2_{i=1}X\cdot P(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \text{Thus:} \\ E(X)=X_1\cdot P(X_1)+X_2\cdot P(X_2) \\ \Rightarrow108=(80)\times(0.3)+X_2\times(0.7) \\ \Rightarrow108=24+X_2\times(0.7) \\ \Rightarrow108-24=X_2\times(0.7) \\ \Rightarrow84=X_2\times(0.7) \\ \Rightarrow X_2\times(0.7)=84 \\ \Rightarrow X_2=\frac{84}{(0.7)}=120 \\ \Rightarrow X_2=120 \end{gathered}[/tex]Therefore, the value of x2 is 120