To find f(5) substitute in the equation the x by 5 and evaluate:
[tex]\begin{gathered} f(5)=3(5)+2 \\ f(5)=15+2 \\ f(5)=17 \end{gathered}[/tex]Then, f(5) is 17Answer:
f(5)=17
Step-by-step explanation:
3(5)+2
15+2
17
Please mark brainliest hope this helps
Only about 16% of all people can wiggle their ears. Is this percent different for millionaires? Of the 342 millionaires surveyed, 58 could wiggle their ears. What can be concluded at the α = 0.01 level of significance?For this study, we should use Select an answerThe null and alternative hypotheses would be: H0: ? Select an answer (please enter a decimal) H1: ? Select an answer (Please enter a decimal)The test statistic ? = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 3 decimal places.)The p-value is ? α Based on this, we should Select an answer the null hypothesis.Thus, the final conclusion is that ...The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the populaton proportion is significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 16%.The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 16%.
We have to perform an hypothesis test on the proportion.
In this case we should use a z-test.
The claim is that the proportion of millonaires that can wiggle their ears is different from 16%.
Then, the null and alternative hypothesis are:
[tex]\begin{gathered} H_0:\pi=0.16 \\ H_a:\pi\ne0.16 \end{gathered}[/tex]The significance level is 0.01.
The sample has a size n = 342.
The sample proportion is p = 58/342 = 0.17.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\frac{\pi(1-\pi)}{n}}=\sqrt{\frac{0.16\cdot0.84}{342}}\approx\sqrt{0.000393}\approx0.0198[/tex]Then, we can calculate the z-statistic as:
[tex]z=\frac{p-\pi-0.5\/n}{\sigma_p}=\frac{0.17-0.16-0.5\/342}{0.0198}\approx\frac{0.0085383}{0.0198}\approx0.431[/tex]This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]2\cdot P(z>0.431)\approx2\cdot0.333\approx0.666[/tex]As the P-value (0.666) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the proportion of millonaires that can wiggle their ears is different from 16%.
Answer:
a) For this study we should use a z-test.
b) H0: p = 0.16
Ha: p ≠ 0.16
c) z = 0.431
d) p-value = 0.666
e) The p-value is greater than α.
f) Based on this we should not reject the null hypothesis.
g) The data suggest the population proportion is not significantly different from 16% at α = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millonaires who can wiggle their ears is different from 16%.
Please answer the question below! I think the answer is 3
To answer this question we will use the following formula to compute the volume of a rectangular prism:
[tex]\text{Volume}=\text{Length}\times\text{Width}\times Height.[/tex]Substituting Length=3, Width=2, and Height=1/2 we get:
[tex]\text{Volume}=3\times2\times\frac{1}{2}\text{.}[/tex]Simplifying the above result we get:
[tex]\text{Volume}=3.[/tex]Answer: The volume is 3 cubic units.
Please help! The last tutors answer was wrong. They want the equation y = and answer for x.
Given that the graph of the Quadratic Equation must pass through these points:
[tex](0,25),(50,200),(100,275)[/tex]• You know that the equation has this form:
[tex]y=ax^2+bx+c[/tex]Where:
[tex]a\ne0[/tex]You can use a calculator to find the corresponding Quadratic Equation that models the given situation:
1. Press the button MODE on your calculator.
2. Choose the option STAT for statistical calculations.
3. Choose the option for Quadratic Regression and enter the coordinates in the table.
4. Press the buttons SHIFT and STAT.
5. Calculate the regression.
You get that:
[tex]\begin{gathered} a=-0.02 \\ b=4.5 \\ c=25 \end{gathered}[/tex]Hence, the Quadratic Equation that models the data is:
[tex]y=-0.02x^2+4.5x+25[/tex]• In order to estimate the population in 2050, you need to substitute this value into the equation:
[tex]x=150[/tex]And evaluate:
[tex]\begin{gathered} y=-0.02(150)^2+4.5(150)+25 \\ y=250 \end{gathered}[/tex]Hence, the answer is:
- Equation:
[tex]y=-0.02x^2+4.5x+25[/tex]- Population in 2050:
[tex]250\text{ }million\text{ }(approximately)[/tex]Solve for the variable:4y+8–2y for y=3
Put y = 3 into the expression:
[tex]\text{ 4y+8-2y}[/tex]It becomes,
[tex]\begin{gathered} 4(3)+8-2(3) \\ 12+8-6 \\ =14 \end{gathered}[/tex]Hence, the answer is 14
Use elimination to solve eachsystem of equations4x - 3y = 112x - y = -8
Given:
The system of equations is,
[tex]\begin{gathered} 4x-3y=11\text{ . . . . . . (1)} \\ 2x-y=-8\text{ . . . . . .(2)} \end{gathered}[/tex]The objective is to solve the equations using the elimination method.
Explanation:
To solve the equations multiply the equation (2) by -3.
[tex]\begin{gathered} -3\lbrack2x-y=-8\rbrack \\ -6x+3y=+24\text{ . . . . (3)} \end{gathered}[/tex]On solving equations (1) and (3),
[tex]\begin{gathered} 4x-3y=11 \\ \frac{-6x+3y=24}{-2x=35} \end{gathered}[/tex]On further solving the above equation,
[tex]x=-\frac{35}{2}[/tex]Substitute the value of x in equation (2).
[tex]\begin{gathered} 2(-\frac{35}{2})-y=-8 \\ -35-y=-8 \\ -y=-8+35 \\ -y=27 \\ y=-27 \end{gathered}[/tex]Hence, the value of x is (-35/2) and the value of y is -27.
A street sign is 115 inches tall. How tall is it in feet and inches
In order to convert from inches to feet and inches, we need to know that 1 foot is equal 12 inches.
Knowing that, in order to convert, let's first divide the number of inches by 12:
[tex]\frac{115}{12}=9.58[/tex]So we have 9 complete units of foot. Now, to find the remaining number of inches, let's subtract the total number of inches (115) by 9 feet in inches (9 * 12):
[tex]\begin{gathered} 115-9\cdot12 \\ =115-108 \\ =7 \end{gathered}[/tex]So the final result is 9 feet 7 inches.
Resolve the vector given in the indicated figure into its x-component and y-component
The x and y components of a vector are given by:
[tex]\begin{gathered} A_x=A\cos\theta \\ A_y=A\sin\theta \end{gathered}[/tex]Where A is the magnitude and theta is the angle measure from the x positive axis counterclockwise. In this case the magnitude is 6694 and the angle is 240°; plugging these values in the expressions above we have:
[tex]\begin{gathered} A_x=6694\cos240=-3347 \\ A_y=6694\sin240=-5797 \end{gathered}[/tex]Therefore, the x and y components of the vector are:
[tex]\begin{gathered} A_x=-3347 \\ A_y=-5797 \end{gathered}[/tex]I just need some help solving this question, i’m not sure what to do
From the double-angle identity,
[tex]cos2x=2*sinx*cosx[/tex]we can rewritte our given equation as:
[tex]4sinxcosx-2cosx=0[/tex]By factoring 2cosx on the left hand side, we have
[tex]2cosx(2sinx-1)=0[/tex]This equation has 2 solutions when
[tex]\begin{gathered} cosx=0\text{ ...\lparen A\rparen} \\ and \\ 2sinx-1=0\text{ ...\lparen B\rparen} \end{gathered}[/tex]From equation (A), we obtain
[tex]x=\frac{\pi}{2}\text{ or }\frac{3\pi}{2}[/tex]and from equation (B), we have
[tex]\begin{gathered} sinx=\frac{1}{2} \\ which\text{ gives} \\ x=\frac{\pi}{6}\text{ or }\frac{5\pi}{6} \end{gathered}[/tex]On the other hand, we can find one more solution from the original equation by substituting x=0, that is,
[tex]\begin{gathered} 2ccos(2\times0)-2cos0=0 \\ which\text{ gives} \\ 2\times1-2\times1=0 \\ so\text{ 0=0} \end{gathered}[/tex]then, x=0 is another solution. In summary, we have obtained the following solutions:
[tex]\begin{gathered} x=0 \\ x=\frac{\pi}{2}\text{or}\frac{3\pi}{2}\text{ and } \\ x=\frac{\pi}{6}\text{or}\frac{5\pi}{6} \end{gathered}[/tex]However, the intersection of the last set is empty. So the unique solution is x=0 as we can corroborate on the following picture:
Therefore, the solution set is: {0}
What is the geometric mean of 7 and 12? a.1b.9.5c.2√21d.4√21
To find the geometric mean,
Simply follow the steps below:
[tex]\frac{x}{7\text{ }}=\frac{12}{x}[/tex][tex]x^2=84[/tex]Take the square root of both-side
[tex]x=\sqrt[]{84}[/tex][tex]=\sqrt[]{4\text{ x 21}}[/tex][tex]=2\sqrt[]{21}[/tex]
Therefore, the correct option is C.2√21
i^333 simplified. pls answer
Given:
[tex]i^{333}[/tex][tex]\begin{gathered} i^{332}i \\ \\ (i^4)^{83}i \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} \text{ Where:} \\ i^4=1 \\ \\ (1)^{83}i \\ \\ =1i \\ \\ =i \end{gathered}[/tex]ANSWER:
[tex]i[/tex]Circle A is congruent to circle P.Which statement is not true?If DC =RQ, then Z CAB ZRPQ.If ZDAC = RPQ, then DC RQ.00If BC = RS, then ZBAC = ZRPS.BIf ZBAC = ZRPS, then BC =RS.
if
[tex]\text{Arc DC}\cong Arc\text{ }RQ[/tex]Then,
[tex]\angle DAC\cong\angle RPQ[/tex]If,
[tex]\text{Arc BC}\cong Arc\text{ RS}[/tex]Then,
[tex]\angle BAC\cong\angle RPS[/tex]With these deductions above the statement that is not true is OPTION A
let g(x) = 3x+2 and f(x)= (x-2)/3. Find the value. f(g(0))a) 0b) -2/3c) 1d) -1
We have two functions:
[tex]\begin{gathered} g\mleft(x\mright)=3x+2 \\ f\mleft(x\mright)=\frac{x-2}{3} \end{gathered}[/tex]We have to calculate f(g(0)).
We can do it like this:
[tex]\begin{gathered} f(g(0))=\frac{g(0)-2}{3} \\ f(g(0))=\frac{\lbrack3(0)+2\rbrack-2}{3} \\ f(g(0))=\frac{0+2-2}{3} \\ f(g(0))=\frac{0}{3} \\ f(g(0))=0 \end{gathered}[/tex]Answer: a) 0
Jessica bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $450 less than the desktop. She paid for the computers using two different financing plans. For the desktop the internet rate was 6.5% per year, and the for laptop it was 9% per year. The total finance charges for one year were $409. How much did each computer cost before finance charges?
SOLUTION:
Step 1 :
In this question, we have that Jessica bought a desktop computer and a laptop computer.
Before finance charges, the laptop cost $450 less than the desktop.
This means that:
[tex]\begin{gathered} \text{Let L = cost of the laptop = D - 450} \\ D=\text{ cost of the desktop } \end{gathered}[/tex]Step 2 :
The total finance charge for one year is given by :
[tex]\begin{gathered} (\text{ 6.5 \% of D ) + ( 9 \% of L ) = 409} \\ (\text{ 0. 065 x D ) + ( 0.09 X ( D - 450 ) ) = 409} \\ 0.065\text{ D + 0.09 D - 40. 5 = 409} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplifying further, we have that:} \\ 0.065\text{ D + 0.09 D = 409 + 40. 5} \\ 0.155\text{ D = 449.5} \end{gathered}[/tex][tex]\begin{gathered} \text{Dividing both sides by 0.155, we have that:} \\ D\text{ =}\frac{449.\text{ 5}}{0.155} \\ D\text{ = }2900 \end{gathered}[/tex]Step 3:
Recall that the cost of the Laptop = D - 450
This means that :
[tex]2900\text{ - 450 = 2450}[/tex]Check:
[tex]\begin{gathered} (\text{ 6. 5\% of 2900 ) + ( 9 \% of 2450 ) } \\ =\text{ 188. 50 + 220. 50 = \$ 409} \end{gathered}[/tex]CONCLUSION:
The cost of the Desktop before the finance charges = $ 2900
The cost of the Laptop before the fiance charges = $ 2450.
is 3 8 9 and 16 in proportion
No, The series 3, 8, 9 and 16 are not in proportion.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
The numbers are;
⇒ 3, 8, 9 and 16
Now,
When two or more ratio are equal to each other then they are in Proportions.
So, We check all the ratio of numbers as;
Ratio of 3 and 8 is;
3 : 8 = 3/8 = 0.375
And, Ratio of 8 and 9 is;
8 : 9 = 8 / 9 = 0.89
And, Ratio of 9 and 16 is;
9 : 16 = 9 / 16
= 0.56
So, The value of all the ratios are not equal.
Hence, All the numbers are not in proportions.
Learn more about the proportion visit:
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express each of the following as Ax^my^n, where xy cannot be equal to 0, A is a real number and m and n are integers
The given expression is:
[tex](\frac{5x^3y}{12y^5x}\div\frac{x^2y}{x^4y^3})\div\frac{75x^{-2}y^{-2}}{9xy^{-1}}[/tex]This can be simplified as
[tex]\begin{gathered} \frac{5x^3\times x^{-1}\times y\times y^{-5}}{12}\times\frac{x^4y^3}{x^2y}\times\frac{9xy^{-1}}{75x^{-2}y^{-2}} \\ \frac{5x^2y^{-4}}{12}\times x^2y^2\times\frac{9x^3y}{75} \\ \frac{45x^7y^{-1}}{900} \\ 0.05x^7y^{-1} \end{gathered}[/tex]where A = 0.05, m = 7, n = -1
Write a equivalent expression to -ab +(-ac)
We are given the following expression:
[tex]-ab+\mleft(-ac\mright)[/tex]We can rewrite the expression by using the sign inside the parenthesis, like this:
[tex]-ab+(-ac)=-ab-ac[/tex]Now, we can take "-a" as a common factor:
[tex]-ab-ac=-a(b+c)[/tex]And thus we get an equivalent expression.
At his new job, Manuel expects to make about $37,850 per year. He is paid bi-weekly. 15% of his gross pay will be withheld for federal income tax; 4% for state income tax and 7.65% for Social Security and Medicare taxes. Calculate his net pay
Manuel earns $37,850 per year. Since he is paid bi-weekly (once in two weeks) and a year has 52 weeks, his gross payment is:
[tex]\frac{37850}{26}=1455.77[/tex]Now, let's add the percentages of each tax:
[tex]15\text{\%}+4\text{\%}+7.65\text{\%}=26.65\text{\%}[/tex]Calculating this percentage of his gross payment, we have:
[tex]1455.77\cdot\frac{26.65}{100}=387.96[/tex]Finally, to find his net pay, let's subtract the taxes from the gross payment:
[tex]1455.77-387.96=1067.81[/tex]His net payment is $1067.81
I need help on net force like if they are pointing eachother do I add it? and how will I know what direction it will move and if it’s unbalanced?
Answer:
Step-by-step explanation:
Michael is 8 years older than his sister .Write an expression for Micheal’s age if his is x years old
Let x be Michael's age. Since MIchael is 8 years older than his syster, we have
[tex]x=8+y[/tex]where y denotes Michael's sister age. Therefore, the searched expression can be: x = 8 + y
The prism shown below is being wrapped for Christmas. How many square feet of wrapping paper will Mrs. Harris need to wrap the prism ?l
I will need to find the Area of each of the shapes first
[tex]\begin{gathered} AreaforA=LXB=5\times10=50in^2 \\ \text{Area for B = L x B = 7 }\times10=70in^2 \\ \text{Area for C = L x B = 5}\times10=50in^2 \\ \text{Area for D = L x B = 7 }\times10=70in^2 \\ \text{Area for E = L x B = 7 }\times5=35in^2 \\ \text{Area for F = L x B = 5}\times7=35in^2 \\ \text{Total Area = 50 + 70 +50 +70 + 35 + 35} \\ \text{Total Area = 310in}^2 \\ I\text{ will have to convert this answer to f}eet. \\ 1\text{ inches = }0.0833333foot \\ 1inches^2\text{ =}0.0069444foot^2 \\ 310ches^2\text{ = x} \\ x\text{ = 310 }\times\text{ 0.0069444}fo \\ x=2.1526foot^2 \end{gathered}[/tex]angles B and P are vertically opposite angles. angle B measures (2×+5) and angle P measures 105 . what is the value of x?
If two angles are vertically opposite, then it means that they are equal. Given that angles B and P are vertically opposite angles, it means that
angle B = angle P
If angle B measures (2x + 5) and angle P measures 105, then
2x + 5 = 105
2x = 105 - 5 = 100
x = 100/2
x = 50
Tyler built 4/6 of his house in 3/4 of a year. How long will it take him to finish building his house?
Let's begin by listing out the given information:
Tyler built (b) = 4/6
Time (t) = 3/4 year
Tyler complete building (c) = 1
Total time (T) =
It will take thi
Write an expression for the general or nth term, an, for the arithmetic sequence.1, 5, 9, 13,...=The general term of the arithmetic sequence is an(Do not factor. Use integers or fractions for any numbers in the expression.)
arithmetic sequence formula
[tex]a_n=a_1+(n-1)d[/tex]where,
a_n=the nᵗʰ term in the sequence
a_1=the first term in the sequence
d=the common difference between terms
n = term position
For the following sequence: 1, 5, 9, 13,...
a_1=the first term in the sequence = 1
d=the common difference between terms = 4
therefore, a general formula for this sequence woul be:
[tex]a_n=1+(n-1)\cdot4[/tex]I need help finding the equation for a tangent line
To answer this question we will use the following slope-point formula for the equation of a line:
[tex]y-y_1=m(x-x_1)\text{.}[/tex]Recall that f'(x) is the slope of the tangent line to the graph at (x,f(x)).
Therefore, the tangent line of y=f(x) at x=2 has a slope of -4 and passes through (-2,-7).
Then, using the slope-point formula for the equation of a line we get:
[tex]y-(-7)=-4(x-(-2))\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} y+7=-4(x+2), \\ y+7=-4x-8. \end{gathered}[/tex]Subtracting 7 from the above equation we get:
[tex]\begin{gathered} y+7-7=-4x-8-7, \\ y=-4x-15. \end{gathered}[/tex]Answer:
[tex]y=-4x-15.[/tex]The exponential function f(x) models the population of a country, f(x), in millions, x years after . Complete parts (a)(e).a. Substitute 0 for x and, find the country's population in The country's population in was nothing million.
The given exponential function is
[tex]f(x)=557(1.026)^x[/tex]Where x is the number of years after 1968
f(x) is the population in millions
a) Substitute x by 0
[tex]f(0)=557(1.026)^0[/tex]Since any number to the power of zero = 1, then
[tex]\begin{gathered} (1.026)^0=1 \\ f(0)=557(1) \\ f(0)=557 \end{gathered}[/tex]The population in 1968 is 557 million
b) At year, 2000 we need to find the value of x
[tex]\begin{gathered} x=2000-1968 \\ x=32 \end{gathered}[/tex]Now let us find f(32)
[tex]\begin{gathered} f(32)=557(1.026)^{32} \\ f(32)=1266.399528 \end{gathered}[/tex]Round it to the nearest whole number
Then the population in 2000 is 1266 million
Find the exact value of each of the remaining trigonometric functions
We have an angle theta and we have to calculate the six trigonometric functions.
We know that:
[tex]\begin{gathered} \sin \theta=\frac{2}{3} \\ \tan \theta<0 \end{gathered}[/tex]As the sine is positive and the tangent is negative, we can conclude that the cosine is negative.
We can find the cosine of theta using the following identity:
[tex]\begin{gathered} \sin ^2\theta+\cos ^2\theta=1 \\ \cos ^2\theta=1-\sin ^2\theta \\ \cos ^2\theta=1-(\frac{2}{3})^2 \\ \cos ^2\theta=1-\frac{4}{9} \\ \cos ^2\theta=\frac{9-4}{9} \\ \cos ^2\theta=\frac{5}{9} \\ \cos \theta=-\frac{\sqrt[]{5}}{3} \end{gathered}[/tex]Now that we know the sine and the cosine, we can derive all the other trigonometric functiosn as:
[tex]\tan \theta=\frac{\sin\theta}{\cos\theta}=\frac{\frac{2}{3}}{-\frac{\sqrt[]{5}}{3}}=-\frac{2}{\sqrt[]{5}}=-\frac{2\sqrt[]{5}}{5}[/tex][tex]\cot \theta=\frac{1}{\tan\theta}=-\frac{\sqrt[]{5}}{2}[/tex][tex]\csc \theta=\frac{1}{\sin \theta}=\frac{3}{2}[/tex][tex]\sec \theta=\frac{1}{\cos\theta}=-\frac{3}{\sqrt[]{5}}=-\frac{3\sqrt[]{5}}{5}[/tex]Answer:
cos θ = -√5/3
tan θ = -2√5/5
cot θ = -√5/2
csc θ = 3/2
sec θ = -3√5/5
Drag each coordinate pair to the correct location on the table. Match the coordinates with the quadrants they lie in. (9, -1) (11 , -1) (1, 2) (-1, 31) (-3, -10) (-3), -1) Quadrant Quadrant II Quadrant III Quadrant IV
(9, -1) is in quadrant 4 (IV)
[tex](1\frac{1}{3},\text{ -1}\frac{1}{3})\text{ is in quadrant 4}[/tex][tex](\frac{1}{3\text{ }},2\frac{1}{3})\text{ is in qudrant 1}[/tex][tex]-1\frac{1}{3},3\frac{1}{3}\text{ is in quadrant 2}[/tex](-3, -10) is in quadrant 3
[tex](-3\frac{1}{3},\text{ -1}\frac{1}{3})\text{ is in quadrant 3}[/tex]I need help on on this answer can you help me
ANSWER :
The answer is Option C.
[tex]undefined[/tex]EXPLANATION :
Using the quadratic formula in finding the values of x :
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the quadratic function.
[tex]-3x^2-4x-4=0[/tex]a = -3, b = -4 and c = -4
[tex]\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(-3)(-4)}}{2(-3)} \\ x=\frac{4\pm\sqrt[]{16-48}}{-6} \\ x=\frac{-4\pm\sqrt[]{-32}}{6} \\ x=\frac{-4\pm4i\sqrt[]{2}}{6} \\ x=\frac{-2\pm2i\sqrt[]{2}}{3} \end{gathered}[/tex]Note that i = √-1
Mr. Connelly had two jobs in 2014. The first job, in which he earned $82,700, was fromJanuary to September, and then the second job he $52,700. Since both employers deductedSocial Security tax, did he overpay? If so, how much should he be refunded? (In 2014, theSocial Security tax was 6.3% with a maximum taxable income of $114,400.)
First determine did he meet the maximum taxable income
82700 + 52700 = 135400
He was over the max
He shuld onlly pay on the max amount
114400 * .063 = 7207.20
He paid on 135400
135400 * .063 =8530.20
Taki the amount he paid and subtract the max he should pay to determine the amount he overpaid
8530.20-7207.2 =1323.00
He overpaid 1323.00
He should be refunded 1323.00
2Last year, Littlefield MiddleSchool had 640 students. Thisyear,it has 480 students. Whatis the percent of decrease
Step 1
Write out all values
Old value = 640
New value = 480
[tex]\begin{gathered} \text{Percentage decrease = }\frac{Old\text{ value - New value}}{\text{old value}}\text{ x 100} \\ \text{ = }\frac{640\text{ - 480}}{640\text{ }}\text{ x 100\%} \\ \text{ = }\frac{160}{640}\text{ x 100\%} \\ \text{ = }\frac{160\text{ x 100}}{640} \\ \text{ = }\frac{16000}{640} \\ =\text{ 25\%} \end{gathered}[/tex]You