The required sample sizes for the confidence intervals are given as follows:
a) Estimate of 38%: 566.
b) No estimate: 601.
How to obtain the required sample sizes?The margin of error for a confidence interval of proportions, using the z-distribution, is calculated as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The parameters of the equation are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The desired margin of error in this problem is of:
M = 0.04.
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For item a, the estimate is of [tex]\pi = 0.38[/tex], hence the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.38(0.62)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.38(0.62)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.38(0.62)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.38(0.62)}}{0.04}\right)^2[/tex]
n = 566.
For item b, when there is no estimate, we use [tex]\pi = 0.5[/tex], hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]
n = 601.
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Instead, now suppose that P(x) = 5band b = 2. What is the weekly percent growth rate in thiscase? What does this mean in every-day language?
According to the given value of b, we can determine the growth rate by substracting 1 from the value of b, that is 2, and converting the result to a percent:
[tex]\begin{gathered} 2-1=1 \\ 1\cdot100=100\% \end{gathered}[/tex]It means that the weekly growth rate is 100%.
In every day language, it means that every week, the number of fish in the lake doubles the number of the last week.
May I please get help with finding out weather each of them can be the HL congruence property
The hypotenuse-leg theorem states that two right right triangles are congruent if the hypotenuse and a leg of one triangle are congruent to the hypotenuse and a leg of the other triangle. Looking at the given options,
For a,
We only know that two legs are congruent. We can't confirm that the hypotenuses are congruent
For b,
two legs and two hypotenuses are congruent
For c, the triangles don't have hypotenuses because they are not right triangles.
For d, the hypotenuses of both triangles is the common line. This means that they are congruent. Two legs are also congruent.
Thus, the correct options are
b. Yes
d. Yes
In ARST, the measure of ZT=90°, the measure of ZR=9°, and RS = 46 feet. Find thelength of ST to the nearest tenth of a foot.
Question:
Solution:
Since it is a right triangle, and the side opposite the angle is unknown, we can use the following trigonometric identity:
[tex]\sin (9^{\circ})=\text{ }\frac{x}{46}[/tex]solving for x, we get:
[tex]x\text{ = sin(9) x 46 = 7.19}\approx7.2[/tex]then the correct solution is:
[tex]x\text{ =}7.2[/tex]
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = xe^(−x^2/98), [−3, 14]
absolute minimum value?
absolute maximum value?
Absolute minimum value and maximum value at f(-3) = -2.7 and
f(14) = 12.14 respectively.
Define function.An association between a number of inputs and outputs is called a function. A function is, to put it simply, an association of inputs where each input is connected to exactly one output. For each function, there is a corresponding range, codomain, and domain.
Given function is -
f(x) = x*e^(−x^2/98)
By differentiating the function, we will get
f'(x) = (1)([tex]e^{-x^{2} /98}[/tex])+ x([tex]\frac{-2x}{98}[/tex] * [tex]e^{-x^{2} /98}[/tex])
f'(x) = ([tex]e^{-x^{2} /98}[/tex] ) - ([tex]\frac{x^{2} }{49}[/tex] * [tex]e^{-x^{2} /98}[/tex])
f'(x) = ([tex]e^{-x^{2} /98}[/tex]) (1 - [tex]\frac{x^{2} }{49}[/tex])
To calculate the maximum and minimum value, (1 - [tex]\frac{x^{2} }{49}[/tex]) must be zero or ([tex]e^{-x^{2} /98}[/tex]) must be zero.
=> (1 - [tex]\frac{x^{2} }{49}[/tex]) =0
=> [tex]\frac{x^{2} }{49}[/tex] = 1
=> [tex]x^{2}[/tex] = 49
=> x = 7 or x= -7
However, -7 is not within our given interval and does not need to be tested. Therefore, put the x = -3,7,14 in given function.
f(-3) = -3 [tex]e^{-9/98}[/tex] = -2.7
f(7) = 7 [tex]e^{-1/2}[/tex] = 4.24
f(14) = 14 [tex]e^{-1/7}[/tex] = 12.14
Absolute minimum value at f(-3) = -2.7 and
Absolute maximum value at f(14) = 12.14
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(300/m) + 44n m=15 n=4
Solve (300/m) + 44n where m = 15 and n = 4
[tex]\begin{gathered} (\frac{300}{m})+44n \\ \text{Substitute for the values of m and n, and you have;} \\ (\frac{300}{15})+44(4) \\ 20+176 \\ 196 \end{gathered}[/tex]The solution to the expression is 196
Find the area of a square with sides 8 centimeters long.
Given:
length of side = 8 cm
Area of square is:
[tex]\begin{gathered} \text{Area}=\text{side}\times\text{side} \\ =8\times8 \\ =64\operatorname{cm} \end{gathered}[/tex]so area of square is 64.
Can you please explain how to differentiate an equation? specifically, how to get from this:h(t) = -16t^2 + 72t + 24 to this:h'(t) = -32t + 72I am a parent trying to help my child. looks vaguely familiar but it's been a long time, if you know what I mean! Thank you!
To differentiate an equation as given you can use the next:
Derivates of powers:
[tex]\begin{gathered} f(x)=x^n \\ f^{\prime}(x)=nx^{n-1} \\ \\ \\ f\mleft(x\mright)=x \\ f^{\prime}(x)=1 \\ \end{gathered}[/tex]Derivate of a constant:
[tex]\begin{gathered} f(x)=c \\ f^{\prime}(x)=0 \end{gathered}[/tex]You have in the given equation two powers (the fist two terms) and a constant (las term (24)):
[tex]\begin{gathered} h^{\prime}(t)=-2(16t)^{2-1}+72(1)+0 \\ \\ h^{\prime}(t)=-32t+72 \end{gathered}[/tex]the solution set of which inequality is represented by the number line below
Let's solve the last inequality
[tex]-2x+5<-3[/tex]First, we subtract 5 from each side
[tex]\begin{gathered} -2x+5-5<-3-5 \\ -2x<-8 \end{gathered}[/tex]Then, we divide the inequality by -2
[tex]\begin{gathered} \frac{-2x}{-2}>-\frac{8}{-2} \\ x>4 \end{gathered}[/tex]The solution to this inequality is all the real numbers greater than 4.
[tex]\begin{gathered} 4x+6>22 \\ 4x>22-6 \\ x>\frac{16}{4} \\ x>4 \end{gathered}[/tex][tex]\begin{gathered} 6x-7\leq17 \\ 6x\leq17+7 \\ x\leq\frac{24}{6} \\ x\leq4 \end{gathered}[/tex]Working on how to plot the axis of symmetry and the vertex for the function:h(x)=(x-5)^2-7
A generic expression of a quadratic is
[tex]f(x)=ax^2+bx+c[/tex]We can write it using the vertex form, that is
[tex]f(x)=a(x-h)^2+k[/tex]The vertex form holds a lot of important properties because it shows us immediately where the vertex is, just by looking at the value of "h" and "k" of the formula, in fact, the vertex of the parabola is
[tex](h,k)[/tex]And the axis of symmetry of a parabola is the x-coordinate of the vertex, then, the axis of symmetry is
[tex]x=h[/tex]But how to identify h and k when we have the parabola in the vertex form? We have the following equation
[tex]h(x)=(x-5)^2-7[/tex]What's the value of the number that sums or subctract the quadratic term? In that case, it's -7, then it's the value of k
[tex]k=-7[/tex]Now to identify the "h" we must take care, it seems like h = -5 because the quadratic term is (x-5)² but we always change the signal of the number inside the quadratic term, if we have -5 inside it, the value of h is 5
[tex]h=5[/tex]Then, the vertex will be
[tex](h,k)=(5,-7)[/tex]The vertex is (5, -7) and the axis of symmetry will be the same value of h, then
[tex]\begin{gathered} x=h \\ \\ x=5 \end{gathered}[/tex]Symmetry and vertex
[tex]\begin{gathered} \text{ vertex: \lparen5, -7\rparen} \\ \\ \text{ axis of symmetry: x = 5} \end{gathered}[/tex]Now, to plot the graph precisely we must find the roots of the parabola, in other words, the value of x that makes h(x) equal to zero:
[tex]\begin{gathered} h(x)=0 \\ \\ (x-5)^2-7=0 \end{gathered}[/tex]Then, we want to solve:
[tex](x-5)^2-7=0[/tex]Put the quadratic term on one side
[tex]\begin{gathered} (x-5)^2=7 \\ \end{gathered}[/tex]Take the square root on both sides
[tex]\begin{gathered} \sqrt{(x-5)^2}=\sqrt{7} \\ \\ |x-5|=\sqrt{7} \end{gathered}[/tex]Be careful! when we do the square root of the quadratic term we must remember to put the modulus. Then we will solve this modular equation:
[tex]|x-5|=\sqrt{7}[/tex]Which is the same as solving to different equations:
[tex]|x-5|=\sqrt{7}\Rightarrow\begin{cases}x-5={\sqrt{7}} \\ x-5=-{\sqrt{7}}\end{cases}[/tex]Then the two solutions are
[tex]\begin{gathered} x=5+\sqrt{7}\approx7.65 \\ \\ x=5-\sqrt{7}\approx2.35 \end{gathered}[/tex]Then we can do the plot of the parabola with a good precision
Or using a graphing calculator
7. Suppose Joanna gets a 10% raise, then a 5% raise. a. What is her raise in total as a percent? (hopefully by now you have learned the answer is not 15% bc percents are tricky) (tip: make up a salary if you need/want to)b. What would her second raise need to be to make the total raise 15%?
Let
x ----> original amount
Part A
1) 10% raise
that means
100%+10%=110%=110/100=1.1
so
1.1x ---> final amount
2) 5% raise
100%+5%=105%=105/100=1.05
so
1.05(1.1x)=1.155x
therefore
1.155=115.5% ------> 115.5-100=15.5%
the answer is 15.5%part B
we have
First, raise ------> 1.1x
second raise
1.1x(a)=1.15
a=1.15/1.1
a=23/22---------> a=1.04545
1.04545-1=0.04545
therefore
The second raise must be 4.545454...%round to two decimal places 4.55%After completing the fraction division 5 divided by 5/3, Miko used the multiplication shown to check her work. 3x5/3=3/1x5/3=15/3 or 5
Answer:
Miko found the correct quotient and checked her work using multiplication correctly
Explanation:
When we divided 5 by 5/3, we get:
[tex]5\div\frac{5}{3}=5\times\frac{3}{5}=\frac{5\times3}{5}=\frac{15}{5}=3[/tex]Therefore, the quotient is 3.
Then, to check the division, we need to multiply the quotient 3 by the divisor 5/3. If we get the dividend 5, the division was correct, so
[tex]3\times\frac{5}{3}=\frac{3}{1}\times\frac{5}{3}=\frac{15}{3}=5[/tex]Therefore, Miko found the correct quotient and checked her work using multiplication correctly.
[tex] \frac{1}{6} (x + 12) = - 4[/tex]Can you please solve it
Problem
[tex] \frac{1}{6} (x + 12) = - 4[/tex]
Solution
For this case we have the following equation given:
[tex]\frac{1}{6}(x+12)=-4[/tex]We can multiply both sides by 6 and we got:
[tex]x+12=-24[/tex]Now we can subtract 12 in both sides and we got:
[tex]x=-24-12=-36[/tex]And the solution for this case would be x=-36
The length of an arc of a circle measures 0.3km. The radius of the circle measures 0.7km. What is the degree measure of the central angle of a circle associated with this arc? Use 3.14 for Π. Round your answer to the nearest tenth.
SOLUTION:
Step 1:
In this question, we are given the following:
The length of an arc of a circle measures 0.3km.
The radius of the circle measures 0.7km.
What is the degree measure of the central angle of a circle associated with this arc? Use 3.14 for Π.
Round your answer to the nearest tenth.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} \text{Length of an arc of a circle = 0. 3 }km \\ \text{Radius of the circle = 0. 7 }km \\ \text{Degr}ee\text{measure of the central angle of a circle = }\theta \\ \pi\text{ = 3. 14} \end{gathered}[/tex][tex]\begin{gathered} \text{Length of Arc , l = }\frac{\theta}{360^0\text{ }}\text{ x 2}\pi r \\ 0.\text{ 3 = }\frac{\theta}{360^0}\text{ x 2 x 3. 14 x 0.7} \end{gathered}[/tex][tex]\begin{gathered} 0.3\text{ = }\frac{\theta\text{ x 4.396}}{360^0} \\ \end{gathered}[/tex]cross-multiply, we have that:
[tex]\begin{gathered} 360\text{ x 0. 3 = 4.396}\theta \\ \text{Divide both sides by 4.396, we have that:} \end{gathered}[/tex][tex]\begin{gathered} \theta\text{ = }\frac{360\text{ X 0. 3}}{4.396} \\ \end{gathered}[/tex][tex]\begin{gathered} \theta=\text{ }\frac{108}{4.396} \\ \end{gathered}[/tex][tex]\begin{gathered} \theta\text{ = 24.5677889} \\ \theta\approx24.6^{0\text{ }}(\text{ to the nearest tenth)} \end{gathered}[/tex]Can someone please help me with these, please? I’ve tried them myself already, but I got confused enough I didn’t end up with an answer
Given:
The cost for a day food, entertainment and hotes is $250.
The cost for round trip air fair is $198.
Explanation:
Let x represents the number of full days that individual can stay at the beach.
The total money available to individual is $1400. So inequality is,
[tex]\begin{gathered} 250\cdot x+198\leq1400 \\ 250x+198\leq1400 \end{gathered}[/tex]Thus inequality for number of days is,
[tex]250x+198\leq1400[/tex]The variable x represent the number of full days that individual can spend at beach trip.
(b)
Solve the inequality for x.
[tex]\begin{gathered} 250x+198-198\leq1400-198 \\ \frac{250x}{250}\leq\frac{1202}{250} \\ x\leq4.808 \end{gathered}[/tex]The maximum whole value of x is 4.
Thus individual can spend 4 complete (full) days at the beach trip.
What matrix results from the elementary row operations represented by
ANSWER:
[tex]-2R_2+3R_1=\begin{pmatrix}-12 & 20 & 8 \\ -8 & 1 & -3\end{pmatrix}[/tex]STEP-BY-STEP EXPLANATION:
We have the following matrix:
[tex]A=\begin{pmatrix}-3 & 5 & 2 \\ 8 & -1 & 3\end{pmatrix}[/tex]We apply the operation where R1 is the first row and R2 is the second row, therefore:
[tex]\begin{gathered} -2R_2=\begin{pmatrix}-3 & \:5 & \:2 \\ \:\:-2\cdot8 & -2\cdot-1 & -2\cdot3\end{pmatrix}=\begin{pmatrix}-3 & \:5 & \:2 \\ \:\:-16 & 2 & -6\end{pmatrix} \\ \\ 3R_1=\begin{pmatrix}3\cdot-3 & 3\cdot5 & 3\cdot2 \\ \:8 & -1 & 3\end{pmatrix}=\begin{pmatrix}-9 & 15 & 6 \\ \:8 & -1 & 3\end{pmatrix} \\ \\ -2R_2+3R_1=\begin{pmatrix}-3 & \:5 & \:2 \\ \:\:-16 & 2 & -6\end{pmatrix}+\begin{pmatrix}-9 & 15 & 6 \\ \:8 & -1 & 3\end{pmatrix}=\begin{pmatrix}-3+-9 & 5+15 & 2+6 \\ -16+\:8 & 2+-1 & -6+3\end{pmatrix} \\ \\ -2R_2+3R_1=\begin{pmatrix}-12 & 20 & 8 \\ -8 & 1 & -3\end{pmatrix} \end{gathered}[/tex]Which of these groups of relative frequencies would be best represented by a pie chart
The data presented by a pie chart is best used when comparing significantly different groups of data.
The correct option would be the one in which all the relative frequencies are different, and they show a significant difference or variation between one another.
From the options provided, the group of relative frequencies that satisfies the problem is:
[tex]17\%,71\operatorname{\%},3\operatorname{\%},9\operatorname{\%}[/tex]OPTION A is correct.
fifty four percent of the items in a refrigerator are dairy products what percent of the items are non dairy products
Given :
54% of the items are dairy products.
Which inequality shows the relationship between the plotted points on the number line? O A. 3-4 O B.-4>3 O c. -4-3 O D. 3 >-4 SUBMIT
The numbers ploted in the number line are -4 and 3
The corresponding inequality will be the one that states a true statement between htese two numbers.
-4 is less than 3 → -4 < 3
You can also say that 3 is creater than -4 → 3 > -4
The correct option is d.
Rita can read 5 pages every minute and has already read 25 pages. Which is equation would match the scenario? *A. y = 25x + 5B. y - 25 = 5xC. y = 30xD. None of the aboveI would really appreciate the help as soon as possible.I will appreciate the help by marking you brainliest.
Given:
Number of pages Rita can read every minute = 5
Pages already read = 25 pages
To find the equation that represents this scenario, use the slope intercept form:
y = mx + b
Where, m is the rate of change.
m = 5
x represents the number of minutes
b represents the number of pages already read.
b = 25
Now, input values into the equation.
We have:
y = 5x + 25
From the choices given, let's rewrite the equation.
Subtract 25 from both sides:
y - 25 = 5x + 25 - 25
y - 25 = 5x
Therefore, the equation from the list that matches the scenario is:
y - 25 = 5x
ANSWER:
B. y - 25 = 5x
tell me if the way I did it include commutative, associative, distributive or combined like terms in my problem
Explanation:
The commutative property said that:
a + b = b + a
The associative property said that:
a + b + c = (a + b) + c
So, in the first step, you apply commutative property when you reorganize the terms, and then, you apply associative property when you add the brackets
Finally, on the second step, you combined like terms because 6x, -x, and 2x are like terms.
I was given this graph:
The points on a graph are frequently used to represent the relationships between two or more objects.
The filled out table exists as follows:
Row 1 = 2, 4, 8
Row 2 = 6, 36, 216
What is meant by graph?A graph is a visual representation or diagram used in mathematics that displays data or values in an organized manner. The points on a graph are frequently used to represent the relationships between two or more objects.
In the first row we have x² = 4. Apply the square root to both sides to get x = 2. It appears your teacher is making x positive.
So we'll have 2 in the first box of row 1.
If x = 2, then x³ = 8 after cubing both sides.
In other words, x³ = 2³ = 2 × 2 × 2 = 8
The value 8 goes in the other box of row 1.
For row 2, we use x = 6 to square that to get x² = 6² = 6 × 6 = 36.
36 will go in the blank box for row 2.
The filled out table exists as follows:
Row 1 = 2, 4, 8
Row 2 = 6, 36, 216
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the measure of an interior angle of a regular polygon is given find the number of sides in the polygon
EXPLANATION.
1.Find the number of sides in the polygon with an interior angle of 160 degrees.
The exercise is as follows:
[tex]\begin{gathered} 160n=(n-2)\times180 \\ 160n=(180\times n)-(180\times2) \\ 160n=180n-360 \\ 160n-180n=-360 \\ -20n=-360 \\ n=\frac{-360}{-20} \\ n=18, \\ \text{the answer is 18 sides } \end{gathered}[/tex]the speed of a stream is 4 mph. A boat travels 6 miles upstream in the same time it takes to travel 14 miles downstream. what is the speed of the boat in still water?
The speed of the boat in still water is 10 mph.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the speed of a stream as 4 mph. A boat travels 6 miles upstream in the same time it takes to travel 14 miles downstream.
Assume the speed of the boat in still water be [x] mph.
We know that -
time [t] = distance[x]/speed[s]
Then, we can write -
6/(x - 4) = 14/(x + 4)
6(x + 4) = 14(x - 4)
6x + 24 = 14x - 56
56 + 24 = 8x
80 = 8x
x = 10 mph
Therefore, the speed of the boat in still water is 10 mph.
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If the ratio of AB to BC is 11:6, at what fraction of AC is point B located? Round to the nearesthundredth, if necessary.
For this case we know that the ratio of AB to BC is 11:6 and we can set up the following ratio:
[tex]\frac{AB}{AC}=\frac{11}{6}[/tex]And we want to identify what fraction of AC is point B located
We can assume that the lenght of AC is lower than AB
So then we can answer this problem with this operation:
[tex]\frac{6}{11}=0.545[/tex]And the answer for this case would be 0.545
On the planet of Mercury, 4-year-olds average 2.9 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.4 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. Find the probability that the child spends less than 2.6 hours per day unsupervised. c. What percent of the children spend over 2.5 hours per day unsupervised. % (Round to 2 decimal places)d. 72% of all children spend at least how many hours per day unsupervised? hours.
Part a.
From the given infomation, the mean is equal to
[tex]\mu=2.9\text{ hours}[/tex]and the standard deviation
[tex]\sigma=1.4\text{ hours}[/tex]Then, the distribution of X is:
[tex]N(2.9,1.4)[/tex]Part b.
In this case, we need to find the following probability:
[tex]P(X<2.6)[/tex]So, in order to find this value, we need to convert the 2.6 hours into a z-value score by means of the z-score formula:
[tex]z=\frac{X-\mu}{\sigma}[/tex]Then, by substituting the given values into the formula, we get
[tex]\begin{gathered} z=\frac{2.6-2.9}{1.4} \\ z=-0.214285 \end{gathered}[/tex]Then, the probability we must find in the z-table is:
[tex]P(z<-0.214285)[/tex]which gives
[tex]P(z<-0.214285)=0.41516[/tex]Therefore, by rounding to 4 decimal places, the answer for part b is: 0.4152
Part c.
In this case, we need to find the following probability
[tex]P(X>2.5)[/tex]Then, by converting 2.5 to a z-value, we have
[tex]\begin{gathered} z=\frac{2.5-2.9}{1.4} \\ z=-0.285714 \end{gathered}[/tex]So, we need to find on the z-table:
[tex]P(z>-0.285714)[/tex]which gives
[tex]P(z\gt-0.285714)=0.61245[/tex]Then, by multiplying this probability by 100% and rounding to the nearest hundreadth,
the answer for part c is: 61.25 %
Part d.
In this case, we have the following information:
[tex]P(z>Z)=0.72[/tex]and we need to find Z. From the z-table, we get
[tex]Z=0.58284[/tex]Then, from the z-value formula, we have
[tex]-0.58284=\frac{X-2.9}{1.4}[/tex]and we need to isolate the amount of hours given by X. Then, by multiplying both sides by 1.4, we obtain
[tex]-0.815976=X-2.9[/tex]Then, X is given by
[tex]\begin{gathered} X=2.9-0.815976 \\ X=2.0840 \end{gathered}[/tex]So, by rounding to 4 decimal places, the answer is: 2.0840 hours.
A TV set is offered for sale for P1, 800 down payment, and P950 every month for thebalance for 2 years. If interest is to be computed at 6% compounded monthly, what isthe cash price equivalent of the TV set?
Answer:
The cash equivalent price of the tv set is P5849.37
Explanation:
The total amount paid monthly is:
The initial down payment of P1800 and 24 payments of P950 (2 years = 24 months)
Then, the price paid with interest is:
[tex]1800+24\cdot950=24600[/tex]
Now, the formula for the monthly compound interest is:
[tex]A=P(1+\frac{r}{12})^{12t}[/tex]Where:
A is the amount after t years
P is the initial amount (what we want to find)
R is the rate of compound in decimal
t is the number of years of compounding
In this case:
• A = 24600 (the total paid if compounded)
,• P is what we want to find
,• r = 0.06 ( to convert percentage to decimal, we divide by 100: 6%/100 = 0.06)
,• t = 24 (2 years)
[tex]\begin{gathered} 24600=P(1+\frac{0.06}{12})^{12\cdot24} \\ . \\ 24600=P\cdot1.005^{288} \\ . \\ P=\frac{24600}{4.2056} \\ . \\ P=5849.373 \end{gathered}[/tex]To the nearest cent, the cash price is 5849.37
how much simple interest can be earned in one year on $800 at 6%
The simple interest is defined as
[tex]I=P\cdot r\cdot t[/tex]Where P is the principal, r is the interest rate and t is times in years. Replacing all given information, and using 0.06 as 6%, we have
[tex]I=800\cdot0.06\cdot1=48[/tex]Therefore, the simple interest is $48.Hi can you please help meThe cut off part:On the same grid, line k passes through
line j and k are perpendicular (option B)
Explanation:J passes through points (8, 2) and (-2, -2)
line K passes through (-4, 3) and (-6, 8)
We need to find the relationship betwen the lines by using the slope from both lines
slope formula is given by:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let's find slope of each line:
[tex]\begin{gathered} \text{for line J: }x_1=8,y_1=2,x_2=-2,y_2\text{ = -}2 \\ \text{slope = m = }\frac{-2-2}{-2-8} \\ \text{slope = }\frac{-4}{-10} \\ \text{slope = 2/5} \\ \\ \text{for line K: }x_1=-4,y_1=3,x_2=-6,y_2\text{ = 8} \\ \text{slope = m = }\frac{8-3}{-6-(-4)} \\ \text{slope = }\frac{5}{-6+4}\text{ = 5/-2} \\ \text{slope = }\frac{\text{-5}}{2} \end{gathered}[/tex]For two lines to be parallel, their slope will be the same:
Since the slopes are not the same, they are not parallel
For two lines to be perpendicular, the slope of one line will be negative reciprocal of the other line:
slope of one line = 2/5
reciprocal of the line = 5/2
negative reciprocal of the line = -5/2
We can see -5/2 is the slope of the other line.
As aresult, line j and k are perpendicular
Factor the given polynomial completely and match your result to the correct answer below.18m³ +24m²-24mSelect one:O a. 6m(m-4)(3m + 1)O b. 6m(3m2 +6m-4)O c.6m(m+2)(3m-2)O d. The polynomial is prime.
Given:
[tex]18m^^3+24m^2-24m[/tex]Required:
We need to factorize the given polynomial completely.
Explanation:
Take out the common multiple 6m.
[tex]18m^3+24m^2-24m=6m(3m^2+4m-4)[/tex][tex]Use\text{ 4m=6m-2m.}[/tex][tex]18m^3+24m^2-24m=6m(3m^2+6m-2m-4)[/tex]Take out the common multiple.
[tex]18m^3+24m^2-24m=6m(3m(m+2)-2(m+2))[/tex][tex]18m^3+24m^2-24m=6m(m+2)(3m-2)[/tex]Final answer:
[tex]6m(m+2)(3m-2)[/tex][tex] - 15 \ \textless \ - 4x - 3[/tex]That's the Math problem
EXPLANATION
Given the inequality
-15 < -4x - 3
Adding +4x to both sides:
-15 + 4x < -4x + 4x -3
Adding +15 to both sides:
-15 + 15 + 4x < -3 + 15
Simplifying:
4x < -15 - 3
Adding like terms:
4x < -15 - 3
Dividing both sides by 4:
x < -18/4
Simplifying the fraction:
x < -4.5
The solution is x<-4.5