So,
Let "t" be the number of minutes she will run today.
Given that she will run more than 11 laps today, then we can set up the inequality:
[tex]\begin{gathered} t>11\cdot4 \\ t>44 \end{gathered}[/tex]This is because 11 laps take 44 minutes to run, and if she will run more than 44 minutes, so t>44.
Shade in 4 of the picture. Shade in 1 of the picture. Shade in 3-4 of the picture.
The first one is correct
In the second one you have to shade one complete circle plus
In the third one you need to shade three complete triangles plus
A crop circle discovered in Cambridge, England, covers approximately 44,100 square feet. What is the approximate diameter of this circle?
We have a circle that has an approximate area of 44100 ft².
We have to calculate the diameter.
We can relate diameter D and area A as:
[tex]A=\frac{\pi}{4}D^2[/tex]We can then calculate D as:
[tex]\begin{gathered} A=\frac{\pi}{4}D^2 \\ D^2=\frac{4A}{\pi} \\ D=\sqrt{\frac{4A}{\pi}} \\ D=\sqrt{\frac{4(44100)}{\pi}} \\ D\approx\sqrt{56149} \\ D\approx237\text{ }ft \end{gathered}[/tex]Answer: the diameter is approximately 237 ft
log32187 = 7 can be expressed as _______A. 37 = 2187B. 32187 = 7C. 73 = 2187D. 72187 = 3
Recall the log to exponential rule:
[tex]\begin{gathered} If \\ \log_aN=x \\ then \\ a^x=N \end{gathered}[/tex]Therefore, we can express the log expression given to be:
[tex]\log_32187=7[/tex]in the exponential form as:
[tex]3^7=2187[/tex]OPTION A is correct.
f(x)=-x+5;g(x)=2f(x) i need to know the horizontal stretch and by. also f(x)=2x+3; g(x)=f(x)+3
For the first equation:
[tex]f(x)=-x+5,g(x)=2f(x)[/tex]That's a vertical stretch by 2. If you change f(x) for 'y' you'll see that more clearly:
[tex]y=-x+5,g(x)=2y[/tex]All 'y' coordinates of the function are now twice as before. This means that the function is stretched vertically.
For the second:
[tex]f(x)=x-4,g(x)=-f(x)[/tex]We'll change f(x) for 'y' too:
[tex]y=x-4,g(x)=-y[/tex]That is a reflection over the x axis. This is because in order to go from y to -y all 'y' coordinates of the points on the function have to change from possitive to negative and from negative to possitive. In a graph:
The product of a number and 3 is the same as the sun of that number and 6
Answer: 3x = 6x
Step-by-step explanation: After you move the variable over you will move 6x so the opposite of 6x is -6x after you subtract -6-3 you should get 3. Thus, the final answer would be 3.
In x - In(x + 1) = 2
Answer: no solution
Step-by-step explanation:
A psychology test has personality questions numbered 1,2,3, intelligence questions numbered 1,2,3,4, and attitude questions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?Provide the final answer as a simplified fraction.
Given:
Personality question = 1,2,3
Intelligence question = 1,2,3,4
Attitude question = 1,2
Find-: what is the probability that the question is an intelligence question OR has an odd number
Sol:
The total number of questions is:
3 Personality, 4 intelligence, and 2 attitudes so the total number of questions is:
[tex]\begin{gathered} =3+4+2 \\ \\ =9 \end{gathered}[/tex]The odd numbers are:
[tex]\begin{gathered} =1,1,1,3,3 \\ \\ \text{ Total 5 questions.} \end{gathered}[/tex]Probability is :
[tex]P=\frac{\text{ Favorable outcome }}{\text{ Total outcome}}[/tex]The probability of an odd number is:
[tex]P=\frac{5}{9}[/tex]The probability of intelligence question of even number is:
[tex]P=\frac{2}{9}[/tex]So required probability is:
[tex]\begin{gathered} =\frac{5}{9}+\frac{2}{9} \\ \\ =\frac{7}{9} \end{gathered}[/tex]Probability is 7/9.
Find the interest earned on a $50,000 deposited for six years at 4 1/8% interest, compounded continuously.
For the given principal $50,000 which was deposited for six years at
4 1/8% interest rate compounded continuously is $14040.97.
As given in the question,
Deposited amount is equal to $50,000
Time period 't' is equal to 6 years
Interest rate 'r' compounded continuously is equal to 4 1/8%
Compounded continuously formula is
A = P[tex]e^{rt}[/tex]
P is the initial amount deposited
P = $50,000
r = 4 1/8%
= 33/8 %
= 0.04125
Substitute the value in the formula we get,
A = ( 50,000 ) × [tex]e^{0.04125 \times 6}[/tex]
⇒ A = 50,000 × [tex]e^{0.2475}[/tex]
⇒ A = 64040.97
Interest =Amount - Principal
⇒ Interest = 64040.97 - 50,000
⇒ Interest = $14040.97
Therefore, For the given principal $50,000 which was deposited for six years at 4 1/8% interest rate compounded continuously is $14040.97.
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Find the value of k that makes f(x) continuous at x = 3
Given:
The function is,
[tex]f(x)=f(x)=\begin{cases}\frac{x-3}{x^2+2x-15},x\ne3 \\ k,x=3\end{cases}[/tex]As the given function is continous at x= 3 ,
[tex]\begin{gathered} \lim _{x\to3}f(x)=k \\ \lim _{x\to3}(\frac{x-3}{x^2+2x-15})=k \end{gathered}[/tex]in a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who who. The claim is that among voters the percentage who believe that they voted for the winning candidate is equal to 43%. find a test statistic for the proportion.
The test statistic is given by
[tex]\frac{\frac{308}{611}-0.43}{\sqrt{\frac{(1-0.43)(0.43)}{611}}}[/tex]The result is 3.699288767
Solve the following(1) 8(11 + 2r) = 12(4/3 r + 22/3)(2) -8(10 + 7k) + 8k = 9 + 4(6 - 12k)
Answers:
(1) r = 0
(2) The equation has no solution
Explanations:
(1) Given the expression:
[tex]8(11+2r)=12(\frac{4}{3}r+\frac{22}{3})[/tex]Removing the brackets, we have:
[tex]88+16r=\frac{48}{3}r+\frac{264}{3}[/tex]Multiply both sides by 3
[tex]\begin{gathered} 264-48r=48r+264 \\ \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} 48r+48r=264-264 \\ 48r=0 \end{gathered}[/tex]Divide both sides by 48
[tex]r=\frac{0}{48}=0[/tex](2) Given the expression:
[tex]-8(10+7k)+8k=9+4(6-12k)[/tex]Remove brackets
[tex]-80-56k+8k=9+24-48k[/tex]Collect like terms
[tex]\begin{gathered} -56k+8k+48k=9+24+80 \\ \end{gathered}[/tex]Simplifying this, the variable k vanishes, leaving us with nothing to find. Therefore, the equation has no solution.
Jada leaves the beach with some seashells. One out of every three of the shells turns out to contain a hermit crab. Write an expression to represent the number of hermit crabs Jada found. Let z represent the total number of seashells she collected.
The expression to represent the number of hermit crabs Jada found is:
1/3z
Given, Jada leaves the beach with some seashells.
One out of every three of the shells turns out to contain a hermit crab.
we are asked to determine the expression to represent the number of hermit crabs Jada found.
Let z represent the total number of seashells she collected.
Hence the expression is:
z × 1/3
= 1/3z
So the total number of seashells Jada collected are 1/3z.
Hence we get the answer as 1/3z
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Which to be used to write an inequality?A. C.=D.+
The symbols > and < can be used to write an inequality. (Options A and B)
4. Given the degree and zeros of a polynomial function, find the standard form of the polynomial.
Degree: 4; zero: -i, 5i
The expanded polynomial is:
x4+
x3 +
x2 +
x +
The equation of the polynomial equation in standard form is P(x) = x⁴ + 6x² + 5
How to determine the polynomial expression in standard form?The given parameters are
Degree = 4
Zero = -i, 5i
There are complex numbers in the above zeros
This means that, the other zeros are
Zeros = -5i and i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = 1 * (x - (-5i)) * (x + 5i) * (x - (-i)) * (x - i)
This gives
P(x) = 1 * (x² + 5) * (x² + 1)
Evaluate the products
P(x) = (x² + 5)(x² + 1)
Express in standard form
P(x) = x⁴ + x² + 5x² + 5
Evaluate the like terms
P(x) = x⁴ + 6x² + 5
Hence, the equation is P(x) = x⁴ + 6x² + 5
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Parker is playing a game in which the object is to obtain a 0 by adding the points scored during each round. (Graph up top ) Based on the points he scored during the first 4 rounds, what score does Parker need on the 5th round?
Objective:
Obtain an score of 0 after add all the scores in all the rounds
Info given:
Round 1: -9
Round 2: 3
Round 3: -8
Round 4: 2
And we want to estimate the score in round 5 in order to obtain a 0 so we can do this:
[tex]-9+3-8+2+x=0[/tex]Where x represent the score required for round 5 and solving we got:
[tex]x=9+8-3-2=12[/tex]So then the score required for round 5 is 12
i will send a pick of the problem
we have that
Verify each statement
1) AE≅DE -----> given ----> is ok
2) BE≅CE ----> given ----> is ok
3) AB=DC----> opposite sides congruent----> is not ok
4) m by vertical angles
5) Δ AEB≅ΔDEC -----> by SAS congruence postulate
therefore
Sarah is not correct
A pizza parlor is considering adding taco pizza and Hawaiian pizza to itsmenu. It surveyed a group of potential customers to find out what theythought, and the results of the survey are shown in the bar graph below, withthe percentage of respondents favoring the addition of each pizza shownabove the corresponding bar.What should we add to our menu?58%47%TacopizzaHawaiianpizzaIf the pizza parlor can make a maximum of 135 pizzas a day, how manyshould they expect will be taco pizzas?
In order to fins the number of pizzas that correspond to Taco pizzas, we can multiply the number of pizzas that the parlor can make, and then using the percentage that corresponded to the selected flavour.
then
[tex]135\cdot58\%=78.3\rightarrow79\text{ taco pizzas}[/tex][tex]7 \sqrt{5 |4| } [/tex]3+6-4÷36×59099m
Graph the system of linear inequalities and shade in the solution set. If there are no solutions, graph the corresponding lines and do not shade in any region X - y > 2 Y < - 1/3x + 1
We need to graph the following inequality system:
[tex]\begin{cases}x-y>2 \\ y<-\frac{1}{3}x+1\end{cases}[/tex]Now we need to isolate the y-variable on the left side for the first equation:
[tex]\begin{cases}yNow we have to graph the boundary lines, which are:[tex]\begin{gathered} y=x-2 \\ y=-\frac{1}{3}x+1 \end{gathered}[/tex]We need to points to graph these equations. We will use the points that have x equal to 0 and y = 0.
For the first equation:
[tex]\begin{gathered} y=0-2 \\ y=-2 \end{gathered}[/tex]The first point is (0,-2).
[tex]\begin{gathered} 0=x-2 \\ x=2 \end{gathered}[/tex]The second point is (2, 0).
For the second equation:
[tex]\begin{gathered} y=-\frac{1}{3}\cdot0+1 \\ y=1 \end{gathered}[/tex]The first point (0,1).
[tex]\begin{gathered} 0=-\frac{1}{3}x+1 \\ \frac{1}{3}x+1 \\ x=3 \end{gathered}[/tex]The second point is (3, 0).
Now we can trace both boundary lines:
Finally we can shade the solution set, which is the region that is below both lines, since both have an "<" signal.
how do I multiplely negative mixed numbers step by step
According to the given data we have the following expression:
(2/5)x -2*4/6
The calculation would be as follows:
1) (2/5)x -8/6
2)(2/5)x=8/6
2x=8/6*5
2x=20/3
x=20/3 / 2
x=3.33333
The value of the x would be x=3.33333
1) multiply -2 times 4/6=-8/6
2)Move -8/6 to other side. Would change sign and would be positive
1. select all equations 2. select all equations 3.select all equations
The correct option C and F
Explanation:x² + 6x = 16
we need to check the other options to find out its equivalence.
a) x² + 6x + 9 = 0
Rewritting the equation above: x² + 6x - 16 = 0
From the above, we can see they are different
b) x² + 6x + 9 = 16
rewritting: x² + 6x + 9 - 16 = 0
x² + 6x - 7 = 0
This is not equivalent to x² + 6x - 16 = 0
c) x² + 6x + 9 = 25
x² + 6x + 9 -25 = 0
x² + 6x -16 = 0
x² + 6x = 16
This is equivalent to x² + 6x = 16
d) (x + 3)² = 0
(x+3)(x+3) = 0
x(x+3)+3(x+3) = 0
x² +3x +3x + 9 = 0
x² + 6x + 9 = 0
This is not equivalent to x² + 6x - 16 = 0
e) (x+3)² = 16
(x+3)(x+3) = 16
x(x+3)+3(x+3) = 16
x² +3x +3x + 9 = 16
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
This is not equivalent to x² + 6x - 16 = 0
f) (x+3)² = 25
(x+3)(x+3) = 25
x(x+3)+3(x+3) = 25
x² +3x +3x + 9 = 25
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This is equivalent to x² + 6x = 16
The correct option C and FF
x(x+3)+3(x+3) = 16
x² +3x +3x + 9 = 16
x² + 6x + 9 = 0
The concert lasted two hours. For how many minutes did the chorus perform alone?
In order to find how many minutes the chorus performed, let's convert the time of 2 hours into minutes.
To do that conversion, we need to know that 1 hour is equal to 60 minutes.
Then, we can write the following rule of three:
[tex]\begin{gathered} \text{hours}\to\text{minutes} \\ 1\text{ hour}\to60\text{ minutes} \\ 2\text{ hours}\to x\text{ minutes} \end{gathered}[/tex]From this rule of three, we can write the following equation and solve it for x:
[tex]\begin{gathered} \frac{1}{2}=\frac{60}{x} \\ 1\cdot x=2\cdot60 \\ x=120 \end{gathered}[/tex]Therefore the chorus performed for 120 minutes.
What is x?5x-35=55-xHow do I get like variables together
hello
this is a simple equation and to solve this, we should first of all collect like terms together
[tex]5x-35=55-x[/tex]step one
collect like terms together
[tex]\begin{gathered} 5x-35=55-x \\ 5x+x=55+35 \\ 6x=90 \end{gathered}[/tex]step two
divide both sides by the coefficient of x
[tex]\begin{gathered} 6x=90 \\ \frac{6x}{6}=\frac{90}{6} \\ x=15 \end{gathered}[/tex]from the calculations above, the value of x is equals to 15
Julianne needs 7 yards of string for her kite. She has 5/8 yards. How many more yards does Julianne need for her kite?
Find out the difference between 7 yards and 5/8 yards
[tex]7-\frac{5}{8}=\frac{8*7-5}{8}=\frac{51}{8}\text{ yd}[/tex]Convert to a mixed number
51/8=(48/8)+(3/8)=6+3/8=6 3/8 yd
therefore
The answer is 6 3/8 ydMark and label the points 1/4 2/4 3/4 and 4/4 on the number line
We can divide a number line from 0 to 1 into 4 parts as label:
1/4, 2/4, 3/4, and 4/4 (which is 1).
Shown below:
Find the equation of a line perpendicular to the given line and pass through the given point. Write equation in slope-intercept form Line y= -4/5x + 2 point, (8,9) Graph
ANSWER
Equation:
[tex]y=\frac{5}{4}x-1[/tex]Graph:
The red line is the graph of the given line and the green line is the graph of the perpendicular line passing through (8, 9).
EXPLANATION
The equation of the line is given in the slope-intercept form,
[tex]y=-\frac{4}{5}x+2[/tex]The slope is -4/5 and the y-intercept is 2.
Two lines are perpendicular if their slopes are opposite reciprocals of each other. Therefore, a perpendicular line to the given line has a slope of 5/4,
[tex]y=\frac{5}{4}x+b[/tex]There is an infinite number of perpendicular lines, but there is only one that passes through the point (8, 9). Replace x and y with the coordinates of this point in the equation above,
[tex]9=\frac{5}{4}\cdot8+b[/tex]And solve for b,
[tex]\begin{gathered} 9=5\cdot2+b \\ 9=10+b \\ 9-10=b \\ -1=b \end{gathered}[/tex]Hence, the equation of the perpendicular line is,
[tex]y=\frac{5}{4}x-1[/tex]4/3x+2/3=1 can someone help me
Given the expression 4/3x+2/3=1, we are to find the value of x from the expression. This is as shown below;
4/3x+2/3=1
subtract 2/3 from both sides
4/3x+2/3-1/3=1-1/3
4/3x = (3-1)/3
4/3x = 2/3
cross multiply
2(3x) = 4(3)
6x = 12
Divide both sides by 6
6x/6 - 12/6
x = 2
Hence the value of x is 2
which of the following does not show the commutative property of addition 9+x=x+9a+b=b+aab=ba3x+4y=4y+3x
The commutative property of addition is such that two or more values or numbers when added up ould alays have the same result no matter how the numbers are rearranged.
Options 1, 2 and 4 shows the commutative property of addition, but OPTION 3 DOES NOT.
The correct answer here is option 3, hich is
ab = ba
A bag contains 25 cookies. There are 15 chocolate chip cookies, 7 peanut butter cookies, and the rest are oatmeal raisin cookies. What is the probability of randomly choosing a chocolate chip or peanut butter cookie from the bag? (Write your answer as a whole percent)
SOLUTION:
Case: Probability
Method:
Total= 25 cookies
Chocolate chip (C)= 15
Peanut butter (P)= 7
Oatmeal raisin (O)= 25 - 15 - 7
Oatmeal raisin= 3
The probability of randomly choosing a chocolate chip or peanut butter cookie from the bag.
[tex]\begin{gathered} Pr(CorP)=\frac{15+7}{25} \\ Pr(CorP)=\frac{22}{25} \end{gathered}[/tex]As a percentage, the percentage equivalence is:
[tex]\begin{gathered} Pr(CorP)=\frac{22}{25}\times100 \\ Pr(CorP)=22\times4 \\ Pr(CorP)=88 \end{gathered}[/tex]Final answer:
88%
homework 7.5 solving radical equations
6=(2x+34)^1/2
Answer:
x=1
Step-by-step explanation: