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Related Questions
Find the value of 53^3 using the identity (x + y)3 = x3 + 3x2y + 3xy2 + y3. Show all work.
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ANSWER:
148877
STEP-BY-STEP EXPLANATION:
We can calculate the value of 53^3, following the following identity:
[tex]\begin{gathered} \mleft(x+y\mright)^3=x^3+3x^2y+3xy^2+y^3 \\ \text{ in this case:} \\ (50+3)^3=50^3+3\cdot50^2\cdot3+3\cdot50\cdot3^2+3^3 \\ (50+3)^3=125000+3\cdot2500\cdot3+3\cdot50\cdot9+27 \\ (50+3)^3=125000+22500+1350+27 \\ (50+3)^3=148877 \\ 53^3=148877 \end{gathered}[/tex]what is the distance between the two points showing on the coordinate plane point below
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Problem
Solution
For this case we can use the following formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]And replacing we got:
[tex]d=\sqrt[]{(4+4_{})^2+(3_{}-3_{})^2}=\sqrt[]{64}=8[/tex]then the best answer would be 8 units
Emiko makes shibori scarves and sells them for $48 each on a website for handmade goods. The expression 48s represents the total price of buying & scarves What do the parts of the expression 48s represent? In the expression 48s s represents the number of scarves and 48 represents the price per scarf Buyers are charged a shipping fee of $4.75 for each scarf order. Which expression can you use to find the total price of a scarf order? 4.758 - 48 4.758 - 48 +8s +4.75
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The total price of scarves is given by
48s.
After adding a shipping fee of $4.75, the expression to represent the total price of a scarf order is,
[tex]\text{Price}=48s+4.75[/tex]The fourth option is the correct answer
Answer: 48s + 4.75
Step-by-step explanation: just did the answer
Part E The baseball team will break even when the amount of money it has received equals the amount of money it spent. In other words, the breaks even when the profit is equal to zero. How many cars does the baseball team have to wash to break even? What point represent value? What does the x-value of this point mean in terms of the problem? it's $5 per car wash and it says they already spent $75
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Answer:
15 cars to break even
Explanation:
The profit of the baseball team can be calculated as:
P = 5x - 75
Where x is the number of cars that they have to wash. So, 5x is the received money and 75 is the spent money.
So, to break even the profit is equal to 0, so the equation is:
0 = 5x - 75
Now, we can solve for x. so, adding 75 on both sides:
0 +75 = 5x - 75 + 75
75 = 5x
Dividing by 5, we get:
75/5 = 5x/5
15 = x
Therefore, the baseball team has to wash 15 cars to break even.
This value of x is the x-intercept of the graph of the profit and it means that when they wash 15 cars, the profit is equal to 0.
Be sure to answer all parts.Carry out each calculation and give the answer using the proper number of significant figures.b. 113.5 x 38 =
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ANSWER:
4313
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]113.5\times38[/tex]We solve as follows:
Therefore, the result is 4313.0
The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Write an exponential decay function, P(t), and use it to approximate the population in 2036.P(t) = _______________, so in 2036 the population is about _________ rabbits.
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Answer:
P(t) = 32308.88, so in 2036 the population is about 32309 rabbits.
Explanation:
An exponential decay function has the following form:
[tex]P(t)=P_0(1-r)^t[/tex]Where P0 is the initial value, r is the percentage of decrease and t is the number of years.
If the population decrease 7.2% every year and the population in 2016 was 144,000, then we can write the function as:
[tex]P(t)=144000(1-0.072)^t[/tex]Where t is the number of years since 2016. So, if we want to approximate the population in 2036, we need to calculate the number of years between 2036 and 2016 as:
2036 - 2016 = 20 years.
Therefore, replacing t by 20, we get that the population in 2036 will be:
[tex]\begin{gathered} P(20)=144000(1-0.072)^{20} \\ P(20)=32308.88 \end{gathered}[/tex]So, the answer is:
P(t) = 32308.88, so in 2036 the population is about 32309 rabbits.
Out of 200 people sampled, 170 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids.Give your answers as decimals, to three places
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The sample proportion is calculated as:
[tex]p=\frac{170}{200}=0.85[/tex]The critical value for significance level = 1 - 0.99 = 0.01, from the z table is z = 2.3263
Therefore, the 99%confidence interval is computed as follows:
[tex]CI=(p-z_c\sqrt{\frac{p(1-p)}{n}},p+z_c\sqrt{\frac{p(1-p)}{n}})[/tex]Where:
p = 0.85
zc = 2.3263
n = 200
Substitute the values we have:
[tex]CI=(0.85-2.3263\sqrt{\frac{0.85(1-0.85)}{200}},0.85+2.3263\sqrt{\frac{0.85(1-0.85)}{200}})[/tex]Simplify:
[tex]\begin{gathered} CI=(0.85-0.0587,0.85+0.0587) \\ CI=(0.7913,0.9087) \end{gathered}[/tex]For 3 decimal places is (0.791, 0.909).
Answer: (0.791, 0.909)
Convert from decimal degrees to degrees-minutes-seconds.Round to the nearest minute.
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Given:
There are given that degree.
[tex]29.75^{\circ}[/tex]Explanation:
According to the question:
We need to convert the given degree to minutes.
Then,
From the given expression:
[tex]29.75^{\operatorname{\circ}}[/tex]Then,
[tex]29.75^{\operatorname{\circ}}=29^{\circ}+0.75^{\circ}[/tex]Then,
To convert the degrees to minutes, we need to multiply by 60.
So,
[tex]\begin{gathered} 29^{\circ}+0.75^{\circ}=29^{\circ}+0.75\times60 \\ =29^{\circ}+45^{\prime} \end{gathered}[/tex]Final answer:
Hence, the value of the given expre
Find two consecutive integers such that four times the greater integer is six less than five times the lesser integer
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Find two consecutive integers such that four times the greater integer is six less than five times the lesser integer
Let
x -----> one integer
x+1 ----> second integer
4(x+1)=5x-6
solve for x
4x+4=5x+6
5x-4x=4-6
x=-2
so
x+1=-2+1=-1
the integers are -1 and -2Find the balance of an account where $3,300 was deposited 3 years ago, earning 4% interest.
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SOLUTION
From the question
Principal, P = $3,300
Time, T = 3 years
Rate, R =4%
Using the simple interest formula
[tex]I=\frac{PRT}{100}[/tex]It follows:
[tex]\begin{gathered} I=\frac{3300\times4\times3}{100} \\ I=396 \end{gathered}[/tex]Therefore the total amount in the account is
[tex]\begin{gathered} A=3300+396 \\ A=3696 \end{gathered}[/tex]Therefore the total amount in the account is $3696
factor x^4-5x^2+4 completely
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Set
[tex]x^4-5x^2+4=0[/tex]Then, if y=x^2;
[tex]\begin{gathered} y=x^2 \\ \Rightarrow x^4-5x^2+4=y^2-5y+4=0 \\ \Rightarrow y^2-5y+4=0 \end{gathered}[/tex]Solve for y using the quadratic equation formula, as shown below
[tex]\begin{gathered} \Rightarrow y=\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot1\cdot4}_{}}{2\cdot1}=\frac{5\pm\sqrt[]{25-16}}{2}=\frac{5\pm3}{2} \\ \Rightarrow y=4,1 \end{gathered}[/tex]Therefore, since y=x^2,
[tex]\begin{gathered} \Rightarrow x^2=4,x^2=1 \\ \Rightarrow x=\pm2,x=\pm1 \end{gathered}[/tex]Finally,
[tex]\Rightarrow x^4-5x^2+4=(x-2)(x+2)(x-1)(x+1)[/tex]The factored form of x^4-5x^2+4 is (x-2)(x+2)(x-1)(x+1)
please help me with this question , thank you so much Item 4 - find the missing part
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the measure of the inscribed angle is half of the m
Ann went bowling and got a score of 210 on her first game. On her second game, her score was 280. What was the percent of increase in her score on the second game?
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ANSWER
33.33%
EXPLANATION
We have that her score on the first game was 210 and on her second game it was 280.
To find the percent of increase, we have to first find the difference between her first and second scores, then divide that by her first score and multiply by 100 (per cent).
Therefore, we have that the percent of increase is:
[tex]\begin{gathered} \frac{280-210}{210}\cdot100 \\ \frac{70}{210}\cdot100 \\ 33.33\text{ \%} \end{gathered}[/tex]That is the percent of increase.
How do I solve this system of equation by graphing Y = x + 312x + y = -6
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Let's pick a method to solve this system:
Let's try substitution:
So x= -9/13 y= 30/13
A piecewise function f(x) is defined as shown.f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayoutWhich table could be used to graph a piece of the function?
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Given:
[tex]\begin{gathered} -\frac{5}{4}x+90,\text{ 0}\leq x<40 \\ -\frac{3}{8}x+75,40\leq x\leq200 \end{gathered}[/tex]Required:
Which table would be used to graph a piece of the function.
Explanation:
Here the function is broken at the three points x=0, x=40, x=200.
So we will choose that table in which the values of x are 0,40,200.
In this table, you can see the values of x are 0,40, and 200.
Final Answer:
The correct answer is
Enter the value in the bank that completes the equation below
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Given the equation;
[tex]4^5\cdot4^3=4^{\text{?}}[/tex]Note that the index powers of two numbers that are equal would be added together. That i;
[tex]\begin{gathered} 4^5\cdot4^3=4^{5+3} \\ 4^5\cdot4^3=4^8 \\ \text{Note that;} \\ (4\times4\times4\times4\times4)\cdot(4\times4\times4)=4\times4\times4\times4\times4\times4\times4\times4 \end{gathered}[/tex]ANSWER:
[tex]4^8[/tex]If this trapezoid is moved through the(x+3, y-2), what will thecoordinates of D' be?translation
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Given the point D = (1, 2), under the translation:
x ⇒ x + 3
y ⇒ y -2
the points D becomes:
D' = (1 + 3, 2 - 2) = (4, 0)
So the answer is D' = (4, 0).
Order these numbers from least to greatest. [tex]6 \frac{1}{11} [/tex][tex] \frac{61}{10} [/tex][tex]6.15[/tex][tex]6.137[/tex]
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We shall first of all, convert all the numbers to the same base. This means we either;
Convert the fractions to decimals OR
Convert the decimals to fractions
Let us therefore convert the decimals to fractions.
[tex]undefined[/tex]which property of equality was used in this expression. 4y = 484y ÷ 4 = 48 ÷ 4
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Explanation:
4y = 48
4y ÷ 4 = 48 ÷ 4
for a = b and c not equal to zero
a/c = b/c
This is a division property of equality.
4y ÷ 4 = 48 ÷ 4
we are dividing both sides by 4
This is also a division property of equality
HELP ME PLEASEEEEEEEEEE
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Answer: D) -2x - 7 < -15
A telemarketers computer selects phone numbers at random. the telemarketer has recorded the number of respondents in each age bracket for one evening in the following table. what is the probability that the next respondent will be 36 or older? Enter a fraction or round your answer to four decimal places if necessary under 18= 2718-25=2126-35=4136-45=60Over 45= 54
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To get the probability, we need two things.
1. The total number of choices
2. The total number of choices considered favorable
Based on the table, there are a total of 203 respondents. Hence, we have 203 people as the total number of choices.
[tex]27+21+41+60+54=203[/tex]Now, based on the question, considered favorable are respondents who are 36 or older. Based on the table, we have a total of 114 respondents who are of this age. Hence, the total number of choices considered favorable is 114.
[tex]\begin{gathered} 36-45:60people \\ over45=54people \\ 60+54=114people \end{gathered}[/tex]The probability that the next respondent will be 36 or older is the ratio of the total number of choices considered favorable over the total number of choices. So, we have:
[tex]P=\frac{114}{203}[/tex]Or in decimal form,
[tex]P=0.5616[/tex]Answer:
The probability that the next respondent will be 36 or older is 114/203 or 0.5616.
4. (02.08 MC)Let f(x) = 4x² + x + 1 and g(x) = x? - 2. Find g(f(x)). Show each step of your work.
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To solve g(f(x)), we will replace the value of x in g(x) with f(x).
[tex]\begin{gathered} g(x)=x^2-2 \\ g(f(x))=(4x^2+x+1)^2-2 \end{gathered}[/tex]Then, simplify.
a. Apply the exponent.
[tex]\begin{gathered} g(f(x))=(4x^2+x+1)(4x^2+x+1)-2 \\ g(f(x))=16x^4+4x^3+4x^2+4x^3+x^2+x+4x^2+x+1-2_{} \end{gathered}[/tex]b. Arrange the terms starting from the highest degree.
[tex]g(f(x))=16x^4+4x^3+4x^3+4x^2+4x^2+x^2+x+x+1-2[/tex]c. Combine like terms.
[tex]undefined[/tex]Evaluate the expression for d = -1.10 – d=
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The expression is given by,
[tex]10-|d|[/tex]Put d=-1 in the above expression to evalute the value of the expression when d=-1.
[tex]10-|-1|[/tex]The modulus of any number is always a positive number with the magnitude rofemaining. Hence,
[tex]10-|-1|=10-1=9[/tex]. Given A(2,5), B(6, -11), C(3, 10), and D(2, 14) determine the relationship between AB and CD?
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hello
we need to find if AB and CD are parallel or perpendiular. to do this, we compare slopes
now we should find slope of AB
[tex]\begin{gathered} \text{slope of AB=}\frac{y_2-y_1}{x_2-x_1} \\ y_2=-11 \\ y_1=5 \\ x_2=6 \\ x_1=2 \\ AB=\frac{-11-5}{6-2} \\ AB=\frac{-16}{4} \\ AB=-4 \end{gathered}[/tex]slope of CD
[tex]\begin{gathered} CD=\frac{y_2-y_1}{x_2-x_1} \\ y_2=14 \\ y_1=10 \\ x_2=2 \\ x_1=3 \\ CD=\frac{14-10}{2-3} \\ CD=\frac{4}{-1} \\ CD=-4 \end{gathered}[/tex]since both slopes are equal, then the lines must be parallel to each other.
you can also use a graph to solve this
greta cut a square from paper that measures 5 inches on each side. she then cut a square that measures 10 inches on each side what the difference in the area of the two squares?
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Area of the square with side 5 inches = 5 x 5 = 25 square feet
Area of the square with side 10 inches = 10 x 10 = 100 square feet
Difference in area of the two squares = 100 - 25 = 75 square feet
S0, the solution is 75 square feet
Andres conducted a scientific experiment. For a certain time, thetemperature of a compound rose 21 degrees every 13 hours. Whatwas the rate, in degrees per hour, that the temperature of thecompound rose? Enter your answer as a whole number, properfraction, or mixed number in simplest form.
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Given:
The temperature of a compound rose is 21 degrees every 13 hours.
Required:
Find the rate, in degrees per hour, that the temperature of the compound rose.
Write the answer as a whole number, proper fraction, or mixed number in simplest form.
Explanation:
Given that the temperature of a compound rose is 21 degrees every 13 hours.
So the rate of the temperature
[tex]\begin{gathered} =\frac{21}{13} \\ =1\frac{8}{13} \\ =1.615384 \end{gathered}[/tex]Final answer:
The rate of the temperature is
[tex]\frac{21}{13}=1\frac{8}{13}=1.615384[/tex]Isabella's parents are starting acollege fund for her today, onher fifth birthday. Assumingthey make no additional depositsor withdrawals, if they want togive her 50 000 Brazilian Realon her eighteenth birthday,how much do they need to deposit now if the bank isoffering an interest rate of 5.5%,compounded monthly. Roundyour answer to the nearestwhole number.
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Today Isabella is having her 5th birthday and her parents want to make one single deposit now so they can collect a total of 50000 Brazilian Real when she is 18.
The investment is thought to be for n=13 years.
The present value (PV) and the future value (FV) of the investment can be calculated by using the compound interest's formula:
[tex]FV=PV(1+\frac{r}{m})^{n\cdot m}[/tex]Where r is the interest rate (APR) offered by the bank, m is the number of compounding periods by each year. Since the compounding period is monthly, then m=12.
If we are given the final value and we want to calculate the present value, then the formula is:
[tex]PV=FV(1+\frac{r}{m})^{-n\cdot m}[/tex]Substituting:
[tex]PV=50000(1+\frac{0.055}{12})^{-13\cdot12}[/tex]Calculating:
[tex]\begin{gathered} PV=50000(1.0045833)^{-156} \\ PV=50000\cdot0.49 \\ PV=24499.59 \end{gathered}[/tex]Isabella's parents should deposit near 24500 Brazilian Reals today
Which type of transformation is represented by the figures in the graph A. dilation and rotation B. Reflection and translation C. Reflection D. Rotation
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To generate the image we need to perform a rotation. To perform a rotation every point on the function or figure must mantain the same distance of the center of rotation and move in a circle around it. We can see that the operation used was a rotation, because we can trace a circle between each point from the function to the image around the origin. The angle of rotation was 180 degrees.
i need help with this please and simple explanation (question 5)
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First thing is to find the coordinates for the two points
(-3,-2) and ( 0,2)
Then we can use the slope formula to determine the slope
m = ( y2-y1)/(x2-x1)
= ( 2 - -2) / ( 0 - -3)
= ( 2+2) / (0+3)
= 4/3
The slope is 4/3
You can also count how many you go up and then how many you go over to get from the left point to the right point.
We go up 4 and then right 3
4/3
The y intercept is where it crosses the y axis.
It crosses at y =2
The slope intercept form of the equation is
y = mx+b where m is the slope and b is the y intercept
y = 4/3x +2
I need help with the entire page , this is for my finals !!
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The Solution:
Given:
[tex]y=16000+5500x[/tex]a.
The explanatory variable is the number of years (x).
b.
The salary (y) when the number of years is 12 years.
[tex]y=16000+5500(12)=\text{ \$}82000[/tex]c.
The annual salary when x = 6 years.
[tex]y=16000+5500(6)=\text{ \$}49000[/tex]d.
The residual for someone who has completed high school education for 6 years.
Residual = actual y value − predicted y value.
[tex]Residual=46000-49000=-\text{\$}3000[/tex]