Solution:
To find the distance between two points, the formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(3,4) \\ (x_2,y_2)=(4,5) \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]d=\sqrt{(4-3)^2+(5-4)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt{2}\text{ units}[/tex]Hence, the answer is
[tex]\sqrt{2}\text{ units}[/tex]Khalil has 2 1/2 hours to finish 3 assignments if he divides his time evenly , how many hours can he give to each
In order to determine the time Khalil can give to each assignment, just divide the total time 2 1/2 between 3 as follow:
Write the mixed number as a fraction:
[tex]2\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}[/tex]Next, divide the previous result by 3:
[tex]\frac{\frac{5}{2}}{\frac{3}{1}}=\frac{5\cdot1}{2\cdot3}=\frac{5}{6}[/tex]Hence, the time Khalil can give to each assignment is 5/6 of an hour.
please help! prove by bubble proof. please show you work
Statement | Reason
Points M and N are on AB | Given
AM ≅ NB | Given
AM + MN ≅ NB + MN | Addition Property of Equality
AM + MN = AN | Segment Addition Postulate
NB + MN = MB | Segment Addition Postulate
AN ≅ MB | Substitution Property of Equality
Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 362 with 54 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
We have to find the 80% confidence interval for a population proportion.
The sample size is n = 362 and the number of successes is X = 54.
Then, the sample proportion is p = 0.149171.
[tex]p=\frac{X}{n}=\frac{54}{362}\approx0.149171[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_s=\sqrt{\frac{p(1-p)}{n}} \\ \sigma_s=\sqrt{\frac{0.149171*0.850829}{362}} \\ \sigma_s=\sqrt{0.000351} \\ \sigma_s=0.018724 \end{gathered}[/tex]The critical z-value for a 80% confidence interval is z = 1.281552.
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z\cdot\sigma_s=0.149171-1.281552\cdot0.018724\approx0.1492-0.0240=0.1252[/tex][tex]UL=p+z\cdot\sigma_s=0.1492+0.0240=0.1732[/tex]As the we need to express it as a trilinear inequality, we can write the 80% confidence interval for the population proportion (π) as:
[tex]0.125<\pi<0.173[/tex]Answer: 0.125 < π < 0.173
State all integer values of X in the interval that satisfy the following inequality.
Solve the inequality
-5x - 5 < 8
for all integer values of x in the interval [-4,2]
We solve the inequality
Adding 5:
-5x - 5 +5 < 8 +5
Operating:
-5x < 13
We need to divide by -5, but we must be careful to flip the inequality sign. It must be done when multiplying or dividing by negative values
Dividing by -5 and flipping the sign:
x > -13 / 5
Or, equivalently:
x > -2.6
I am here, I'm correcting the answer. the interval was [-4,2] I misread the question. do you read me now?
Any number greater than -2.6 will solve the inequality, but we must use only those integers in the interval [-4,2]
Those possible integers are -4, -3, -2, -1, 0, 1, 2
The integers that are greater than -2.6 are
-2, -1, 0, 1, 2
This is the answer.
Review: Solve for Area AND Circumference. A giant holiday cookie has a radius of 5 inches. What is the area of the cookie? What is the circumference of the cookie?
Remember that the formual for the area of a circle is:
[tex]A=\pi r^2[/tex]And the formula for the circumference is:
[tex]C=2\pi r[/tex]Using this formulas and the data given,
[tex]\begin{gathered} A=\pi(5^2)\Rightarrow A=78.54 \\ C=2\pi(5)\Rightarrow A=31.42 \end{gathered}[/tex]The cookie has an area of 78.54 square inches and a circumference of 31.42 inches
Hello! Is it possible to get help on this question?
To determine the graph that corresponds to the given inequality, first, let's write the inequality for y:
[tex]2x\le5y-3[/tex]Add 3 to both sides of the expression
[tex]\begin{gathered} 2x+3\le5y-3+3 \\ 2x+3\le5y \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{2}{5}x+\frac{3}{5}\le\frac{5}{5}y \\ \frac{2}{5}x+\frac{3}{5}\le y \end{gathered}[/tex]The inequality is for the values of y greater than or equal to 2/5x+3/5, which means that in the graph the shaded area will be above the line determined by the equation.
Determine two points of the line to graph it:
-The y-intercept is (0,3/5)
- Use x=5 to determine a second point
[tex]\begin{gathered} \frac{2}{5}x+\frac{3}{5}\le y \\ \frac{2}{5}\cdot5+\frac{3}{5}\le y \\ 2+\frac{3}{5}\le y \\ \frac{13}{5}\le y \end{gathered}[/tex]The second point is (5,13/5)
Plot both points to graph the line. Then shade the area above the line.
The graph that corresponds to the given inequality is the second one.
What is the value of 12x if x = −5?
−60 −17 −125 −47
Answer:
-60
Step-by-step explanation:
Okay so I’m doing this assignment and got stuck ont his question can someone help me out please
ANSWER
[tex]B.\text{ }\frac{256}{3}[/tex]EXPLANATION
We want to find the value of the function for F(4):
[tex]F(x)=\frac{1}{3}*4^x[/tex]To do this, substitute the value of x for 4 in the function and simplify:
[tex]\begin{gathered} F(4)=\frac{1}{3}*4^4 \\ F(4)=\frac{1}{3}*256 \\ F(4)=\frac{256}{3} \end{gathered}[/tex]Therefore, the answer is option B.
Explain how to translate the point (5, 2) with the transformations: D2 and r(180,0). Make sure toexplain, in words, how you got your final answer, including where the point was after the firsttransformation.Edit ViewInsertFormat Tools TableΑν12ptvParagraph | BIUTv
We will have the following:
First: We dilate by a factor of 2, then we would have:
[tex](10,4)[/tex]Second: We rotate by 180°:
[tex](-10,-4)[/tex]determine how many vertices and how many edges the graph has
in the given figure,
there are 4 vertices
and there are 3 edges.
thus, the answer is,
vertiev
Write the sequence {15, 31, 47, 63...} as a function A. A(n) = 16(n-1)B. A(n) = 15 + 16nC. A(n) = 15 + 16(n-1)D. 16n
To find the answer, we need to prove for every sequence as:
Answer A.
If n=1 then:
A(1) = 16(1-1) = 16*0 = 0
Since 0 is not in the sequence so, this is not the answer
Answer B.
If n=1 then:
A(1) = 15 + 16*1 = 31
Since 31 is not the first number of the sequence, this is not the answer
Answer D.
If n=1 then:
16n = 16*1 = 16
Since 16 is not in the sequence so, this is not the answer
Answer C.
If n = 1 then:
A(1) = 15 + 16(1-1) = 15
A(2) = 15 + 16(2-1) = 31
A(3) = 15 + 16(3-1) = 47
A(4) = 15 + 16(4-1) = 63
So, the answer is C
Answer: C. A(n) = 15 + 16(n-1)
Instructions: Factor 2x2 + 252 + 50. Rewrite the trinomial with the c-term expanded, using the two factors. Answer: 24 50
Given the polynomial:
[tex]undefined[/tex]Elisa purchased a concert ticket on a website. The original price of the ticket was $95. She used a coupon code to receive a 10% discount. The website applied a 10% service fee to the discounted price. Elisa's ticket was less than the original by what percent?
The price of the ticket after the cupon is:
[tex]95\cdot0.9=85.5[/tex]To this price we have to add 10%, then:
[tex]85.5\cdot1.1=94.05[/tex]Hence the final cost of the ticket is $94.05.
To find out how less is this from the orginal price we use the rule of three:
[tex]\begin{gathered} 95\rightarrow100 \\ 94.05\rightarrow x \end{gathered}[/tex]then this represents:
[tex]x=\frac{94.05\cdot100}{95}=99[/tex]Therefore, Elisas's ticket was 1% less than the orginal price.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x+9y=63
Answer: y = 63x - 180
Step-by-step explanation: y = mx + b ------(i)
Step one: y = 9, x = 3
9 = 63 (3) + b
9 = 189 + b
-180 = b
b = -180
y = 63x - 180
Answer is
y = -1/3x-6
what does y= 75-29 equal?
Starting with the expression:
[tex]y=75-29[/tex]Substract the numbers to find the value of y:
[tex]y=46[/tex]Answer:
if y = 75-29 the we subtract 29 from 15
75-29=46
y=46
How many true, real number solutions does the equation n + 2 = -16-5n have?solution(s)
The equation is
n + 2 = - 16 - 5n
By collecting like terms, we have
n + 5n = - 16 - 2
6n = - 18
Dividing both sides of the equation by 6, we have
6n/6 = - 18/6
n = - 3
It has only one solution
2x^3-16x^2-40x=0 factor
The given expression is
[tex]2x^3-16x^2-40x=0[/tex]We extract the common factor 2x.
[tex]\begin{gathered} 2x(x^2-8x-20)=0 \\ 2x=0\rightarrow x=0 \\ x^2-8x-20=0 \end{gathered}[/tex]The first solution is 0.
Now, we solve the quadratic expression. We have to find two numbers whose product 20 and whose difference is 8. Those numbers are 10 and 2.
[tex]x^2-8x-20=(x-10)(x+2)[/tex]Hence, the given expressions expressed, as factors, is[tex]2x^3-16x^2-40x=x(x-10)(x+2)[/tex]Function f is defined by f(x) = 2x – 7 and g is defined by g(x) = 5*
Answer
f(3) = -1, f(2) = -3, f(1) = -5, f(0) = -7, f(-1) = -9
g(3) = 125, g(2) = 25, g(1) = 5, g(0) = 1, g(-1) = 0.2
Step-by-step explanation:
Given the following functions
f(x) =2x - 7
g(x) = 5^x
find f(3), f(2), f(1), f(0), and f(-1)
for the first function
f(x) = 2x - 7
f(3) means substitute x = 3 into the function
f(3) = 2(3) - 7
f(3) = 6 - 7
f(3) =-1
f(2), let x = 2
f(2) = 2(2) - 7
f(2) = 4 - 7
f(2) =-3
f(1) = 2(1) - 7
f(1) = 2 - 7
f(1) =-5
f(0) = 2(0) - 7
f(0) =0 - 7
f(0) = -7
f(-1) = 2(-1) - 7
f(-1) = -2 - 7
f(-1) = -9
g(x) = 5^x
find g(3), g(2), g(1), g(0), and g(-1)
g(3), substitute x = 3
g(3) = 5^3
g(3) = 5 x 5 x 5
g(3) = 125
g(2) = 5^2
g(2) = 5 x 5
g(2) = 25
g(1) = 5^1
g(1) = 5
g(0) = 5^0
any number raised to the power of zero = 1
g(0) = 1
g(-1) = 5^-1
g(-1) = 1/5
g(-1) = 0.2
Andre and Elena are each saving money, Andre starts with 100 dollars in his savings account and adds 5 dollars per week, Elena starts with 10 dollars in her savings account and adds 20 dollars each week.After 4 weeks who has more money in their savings account?? Explain how you know.After how many weeks will Elena and Andre have the same amount of money in their savings account? How do you know?
We can model each savings account balance in function of time as a linear function.
Andre starts with $100 and he adds $5 per week. If t is the number of weeks, we can write this as:
[tex]A(t)=100+5\cdot t[/tex]In the same way, as Elena starts with $10 and saves $20 each week, we can write her balance as:
[tex]E(t)=10+20\cdot t[/tex]We can evaluate their savings after 4 weeks (t=4) as:
[tex]\begin{gathered} A(4)=100+5\cdot4=100+20=120 \\ E(4)=10+20\cdot4=10+80=90 \end{gathered}[/tex]After 4 weeks, Andre will have $120 and Elena will have $90.
We can calculate at which week their savings will be the same by writing A(t)=E(t) and calculating for t:
[tex]\begin{gathered} A(t)=E(t) \\ 100+5t=10+20t \\ 5t-20t=10-100 \\ -15t=-90 \\ t=\frac{-90}{-15} \\ t=6 \end{gathered}[/tex]In 6 weeks, their savings will be the same. We know it beca
A particle is moving along the x-axis and the position of the particle at the time t is given by x (t) whose graph is shown above. Which of the following is the best estimate for the speed of the particle as time t=4?
Given:
We are given the x(t) vs time curve.
To find:
Speed of particle at t = 4
Step by step solution:
We know that the slope of x-t curve represents the speed of the particle.
To calculate the speed of the particle at t = 4, We will calculate the slope of the curve at t = 4
[tex]\begin{gathered} Slope=\frac{y_2-y_1}{x_2-x_1} \\ \\ Slope=\frac{40-10}{6-0} \\ \\ Slope=\frac{30}{6} \\ \\ Slope\text{ = 6} \end{gathered}[/tex]From here we can say that the slope of the curve between x = 0 and x = 6 is equal to 5.
So the value of speed is also 5 units, Which is equal to option A.
What is 4527 written in scientific notation?A.4.527B.4.527 x 10*2C.4.527 x 10*3D.4.527 x 10*4
Solution
- The question would like us to convert the number 4527 to scientific notation.
- In order to write a number to its scientific notation, we need to follow these steps:
1. Move the decimal place to the right of the first digit of the number. Make sure you count each step as you move the decimal point from right to left or left to right.
2. The number of steps corresponds to the exponent of 10 that multiplies the decimal form of the original number.
- We can apply these steps to solve the question given as follows:
- Thus, we have that the scientific notation of the number 4527 is
[tex]4.527\times10^3[/tex]Final Answer
The scientific notation of the number 4527 is
[tex]4.527\times10^3\text{ (OPTION C)}[/tex]
which of the following describes the two spheres A congruentB similarC both congruent and similarD neither congruent nor similar
The two spheres are similar since they have a proportion of their radius. This proportion is 9/6 (3/2) or 6/9 (2/3).
They are not congruent. They do not have the same radius.
Therefore, the spheres are similar.
An outdoor equipment store surveyed 300 customers about their favorite outdoor activities. The circle graph below shows that 135 customers like fishing best, 75 customers like camping best, and 90 customers like hiking best.
it is given that,
total customer surveyed is 300 customers
also, it is given that,
135 customers like fishing best, 75 customers like camping best, and 90 customers like hiking best.
the total 300 customers representing the whole circle and circle has a complete angle of 360 degrees
so, 300 customers = 360 degrees,
1 customer = 360/300
= 6/5 degrees,
so, for fishing
135 customer = 135 x 6/5 degrees
= 27 x 6
= 162 degrees,
so, for camping
75 x 6/5 = 90 degrees,
for hiking
90 x 6/5 = 108 degrees,
3. Identify the solution to the system of equations by graphing:(2x+3y=12y=1/3 x+1)
Given equations are
[tex]2x+3y=12[/tex][tex]y=\frac{1}{3}x+1[/tex]The graph of the equations is
Red line represents the equation 2x=3y=12 and the blue line represents the equation y=1/3 x=1.
A study is done on the number of bacteria cells in a petri dish. Suppose that the population size P(1) after t hours is given by the following exponential function.P (1) = 2000(1.09)Find the initial population size.Does the function represent growth or decay?By what percent does the population size change each hour?
Given:
the population size P(1) after t hours is given by the following exponential function:
[tex]P(1)=2000(1.09)[/tex]Find the initial population size?
The initial size = 2000
Does the function represent growth or decay?
Growth, Because the initial value multiplied by a factor > 1
By what percent does the population size change each hour?
The factor of change = 1.09 - 1 = 0.09
So, the bacteria is increasing by a factor of 9% each hour
Let f(x) = 8x^3 - 3x^2Then f(x) has a relative minimum atx=
1) To find the relative maxima of a function, we need to perform the first derivative test. It tells us whether the function has a local maximum, minimum r neither.
[tex]\begin{gathered} f^{\prime}(x)=\frac{d}{dx}\mleft(8x^3-3x^2\mright) \\ f^{\prime}(x)=\frac{d}{dx}\mleft(8x^3\mright)-\frac{d}{dx}\mleft(3x^2\mright) \\ f^{\prime}(x)=24x^2-6x \end{gathered}[/tex]2) Let's find the points equating the first derivative to zero and solving it for x:
[tex]\begin{gathered} 24x^2-6x=0 \\ x_{}=\frac{-\left(-6\right)\pm\:6}{2\cdot\:24},\Rightarrow x_1=\frac{1}{4},x_2=0 \\ f^{\prime}(x)>0 \\ 24x^2-6x>0 \\ \frac{24x^2}{6}-\frac{6x}{6}>\frac{0}{6} \\ 4x^2-x>0 \\ x\mleft(4x-1\mright)>0 \\ x<0\quad \mathrm{or}\quad \: x>\frac{1}{4} \\ f^{\prime}(x)<0 \\ 24x^2-6x<0 \\ 4x^2-x<0 \\ x\mleft(4x-1\mright)<0 \\ 0Now, we can write out the intervals, and combine them with the domain of this function since it is a polynomial one that has no discontinuities:[tex]\mathrm{Increasing}\colon-\infty\: 3) Finally, we need to plug the x-values we've just found into the original function to get their corresponding y-values:[tex]\begin{gathered} f(x)=8x^3-3x^2 \\ f(0)=8(0)^3-3(0)^2 \\ f(0)=0 \\ \mathrm{Maximum}\mleft(0,0\mright) \\ x=\frac{1}{4} \\ f(\frac{1}{4})=8\mleft(\frac{1}{4}\mright)^3-3\mleft(\frac{1}{4}\mright)^2 \\ \mathrm{Minimum}\mleft(\frac{1}{4},-\frac{1}{16}\mright) \end{gathered}[/tex]4) Finally, for the inflection points. We need to perform the 2nd derivative test:
[tex]\begin{gathered} f^{\doubleprime}(x)=\frac{d^2}{dx^2}\mleft(8x^3-3x^2\mright) \\ f\: ^{\prime\prime}\mleft(x\mright)=\frac{d}{dx}\mleft(24x^2-6x\mright) \\ f\: ^{\prime\prime}(x)=48x-6 \\ 48x-6=0 \\ 48x=6 \\ x=\frac{6}{48}=\frac{1}{8} \end{gathered}[/tex]Now, let's plug this x value into the original function to get the y-corresponding value:
[tex]\begin{gathered} f(x)=8x^3-3x^2 \\ f(\frac{1}{8})=8(\frac{1}{8})^3-3(\frac{1}{8})^2 \\ f(\frac{1}{8})=-\frac{1}{32} \\ Inflection\: Point\colon(\frac{1}{8},-\frac{1}{32}) \end{gathered}[/tex]Nora needs to order some new supplies for the restaurant where she works. Therestaurant needs at least 478 forks. There are currently 286 forks. If each set on salecontains 12 forks, write and solve an inequality which can be used to determine s, thenumber of sets of forks Nora could buy for the restaurant to have enough forks.<
Nora needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 478 forks. There are currently 286 forks. If each set on sale
contains 12 forks, write and solve an inequality which can be used to determine s, the
number of sets of forks Nora could buy for the restaurant to have enough forks.
Let
s -----> the number of sets of forks Nora could buy for the restaurant to have enough forks
so
the inequality that represent this situation is
[tex]286+12s\ge478[/tex]solve for s
[tex]\begin{gathered} 12s\ge478-286 \\ 12s\ge192 \\ s\ge16 \end{gathered}[/tex]the minimum number of sets is 16the city pays students $50 per day to serve snow cones at the local summer festival. Analyze the potential earnings of a student who works the whole week of the festival if working partial days is not permitted. this situation can be modeled by the function f(x)=50x.What is a reasonable maximum value for the dependent variable? Explain how you arrived at your answer.
Given:
The per day earning $50
The function is
[tex]f(x)=50x[/tex]Find-:
The maximum value of earning
Explanation-:
The function is
[tex]f(x)=50x[/tex]Where,
[tex]x=\text{ Number of days}[/tex]The students work for a whole week.
[tex]1\text{ week }=7\text{ Days}[/tex]So the maximum value is
[tex]\begin{gathered} f(x)=50x \\ \\ x=7 \\ \\ f(7)=50\times7 \\ \\ f(7)=350 \end{gathered}[/tex]The maximum earning is $350
Write a division equation that represents the equation, How many 3/4 are in 10/9?
Given:
The number of 3/4 in 10/9.
To find the division equation that represents the given problem:
That is a number that is multiplied by 3/4 to obtain 10/9.
We need to find the number.
[tex]x\times\frac{3}{4}=\frac{10}{9}[/tex]Thus, the division equation will be,
[tex]x=\frac{10}{9}\div\frac{3}{4}[/tex]Translate the triangle.Then enter the new coordinates.A (3,4)C(-5,0)<4,2>B(-12)A' ([?], [])B'([ ], [ ])C'([ ], [])
Given:
The coordinates of the triangle are A(-3,4), B(-1,2), and C(-5,0).
Required:
We need to translate the given triangle to <4,2> 4 units right and 2 units up.
Explanation:
The image of the point can be written as follows.
[tex](x,y)\rightarrow(x+4,y+2)[/tex]Consider point A(-3,4).
[tex]A(-3,4)\rightarrow A^{\prime}(-3+4,4+2)[/tex][tex]A(-3,4)\rightarrow A^{\prime}(1,6)[/tex]Consider point B(-1,2).
[tex]B(-1,2)\rightarrow B^{\prime}(-1+4,2+2)[/tex][tex]B(-1,2)\rightarrow B^{\prime}(3,4)[/tex]Consider point C(-5,0).
[tex]C(-5,0)\rightarrow C^{\prime}(-5+4,0+2)[/tex][tex]C(-5,0)\rightarrow C^{\prime}(-1,2)[/tex]Final answer:
A'(1, 6), B'(3, 4) and C'(-1, 2).