Since the coordinates are written as (x,y), for the point (5,1) we have that:
[tex]\begin{gathered} x=5 \\ y=1 \end{gathered}[/tex]Therefore, this is a solution to the equation y=1.
Then, the answer is yes.
Suzan collected 560 milliliters of rainwater on Saturday. She collected 3.5 liters of rainwater on Sunday.How many total milliliters of rainwater did Suzan collect on Saturday and Sunday?A.910B.4,060C.4,600D.9,100
It's easy to see that to obtain the total of milliliters of rainwater that Suzan collected on Saturday and Sunday is the sum of the milliliters that Suzan collected each day.
The problem that we need to be careful about is the units. So we need to pass all the numbers to milliliters, we already have one in this unit then we just need to transform one:
[tex]3.5L\ast\frac{1000mL}{1L}=3500mL[/tex]Now we can use the sum as:
[tex]mL\text{ total=}3500mL+560mL=4060mL[/tex]Then the correct answer is B, 4060 mL.
A parallelogram has a height of 7 meters and an area of 35 square meters. what would the sum of the bases be for a trapezoid with the same height and area as the parallelogram?
The height of trapezoid is h = 7 m.
The area of trapezoid is A = 35 m^2.
The formula for the area of trapezoid is,
[tex]A=\frac{a+b}{2}\cdot h[/tex]Here, a and b are length of bases of trapezoid.
Substitute the values in the formula to obtain the sum of bases of trapezoid.
[tex]\begin{gathered} 35=\frac{a+b}{2}\cdot7 \\ \frac{a+b}{2}=\frac{35}{7} \\ a+b=5\cdot2 \\ =10 \end{gathered}[/tex]So sum of bases of trapezoid is equal to 10 meters.
Solve the following system of linear equations using elimination. -3x + 3y=-3 2x-y=0
The system of equations is
[tex]\begin{gathered} -3x+3y=-3\Rightarrow(1) \\ 2x-y=0\Rightarrow(2) \end{gathered}[/tex]Since all terms in equation 1 can divide by 3, then
Divide each term in equation 1 by 3
[tex]\begin{gathered} \frac{-3x}{3}+\frac{3y}{3}=\frac{-3}{3} \\ -x+y=-1\Rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3) to eliminate y
[tex]\begin{gathered} (2x-x)+(-y+y)=(0-1) \\ x+0=-1 \\ x=-1 \end{gathered}[/tex]Substitute x by -1 in equation (2) to find y
[tex]\begin{gathered} 2(-1)-y=0 \\ -2-y=0 \end{gathered}[/tex]Add y to both sides
[tex]\begin{gathered} -2-y+y=0+y \\ -2+0=y \\ -2=y \\ y=-2 \end{gathered}[/tex]The solution of the given system of equations is (-1, -2)
A researcher studying public opinion of proposed social security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases? b. 25% of all adult Americans support the changes. b. The researcher must ask [] more American adults.
b) We have 25% support the changes, therefore solve:
[tex]np(1-p)=10[/tex]where p =25% = 0.25
So
[tex]\begin{gathered} n(0.25)(1-0.25)=10 \\ n(0.25)(0.75)=10 \\ n(0.1875)=10 \\ \frac{n(0.1875)}{0.1875}=\frac{10}{0.1875} \\ n=53.3\approx54 \end{gathered}[/tex]Need 54 people but already have 50, then:
[tex]54-50=4[/tex]Answer: 4
compare the elevation of death valley and westmorland using< or >
Answer:
If D represent the elevation of Death valley , California and W represent the elevation of Westmorland, California.
So, we would have;
[tex]DWhich means that;the elevation of Death valley < the elevation of Westmorland
Explanation:
Given that the elevation of Death valley , California is -282 feet
[tex]D=-282[/tex]And the elevation of Westmorland, California is -157 feet;
[tex]W=-157[/tex]And we know that -282 ft is less than -157 ft.
[tex]-282<-157[/tex]Therefore, the elevation of Death valley , California is less than the elevation of Westmorland, California.
So, if D represent the elevation of Death valley , California and W represent the elevation of Westmorland, California.
So, we would have;
[tex]DWhich means that;the elevation of Death valley < the elevation of Westmorland
what will the deposit have to be if you want to have 12000 in an account that will earn 8.55% compounded weekly at the end of 5 years
Given:
The expected deposit =?
This is also referred to the principal
r = rate = 8.55%
t = time = 5years
n = we
What are inequalites, and a example of one.
Inequalities are relationships like equalities, what makes it different from equalitites is that on both sides are different expressions that allows to comparate them without been equal, for this we have 4 types
≤ less or equal than
≥ greater or equal to
< less than
> greater than
some examples are:
[tex]\begin{gathered} 3x-3<50 \\ 5x-45>33x \\ x^2-15x<34 \end{gathered}[/tex]Another difference between inequalities and equalities is that in equalities we obtain 1,2 or 3 solutions accronding to the degree of the equation, in inequalities we can obtain infinite number of solutions.
The cube root of our varies inversely with the square of S which to equations model this relationship?
The question states as follows;
"The cube root of r varies inversely with the square of s."
The general form of an inverse relationship is shown below;
[tex]y=\frac{k}{x}[/tex]Substituting the variables, we would now have;
[tex]\sqrt[3]{r}=\frac{k}{s^2}[/tex]Therefore, the third option is correct.
Also;
[tex]\begin{gathered} \sqrt[3]{r}=\frac{k}{s^2} \\ \text{Observe that}_{} \\ \sqrt[3]{r}=r^{\frac{1}{3}} \end{gathered}[/tex]Therefore, we can alo have the expression;
[tex]\begin{gathered} r^{\frac{1}{3}}=\frac{k}{s^2} \\ \text{Cross multiply, and we'll have;} \\ s^2r^{\frac{1}{3}}=k \end{gathered}[/tex]The fifth option is also correct.
ANSWER:
The third and fifth options are both correct models of the inverse relationship given.
Which represents the inverse of the function f(x) = 4x?h(x) = x + 4Oh(x) = X-4Oh(x) = 2xh(x) =17 1x
f(x) = 4x
To find the inverse of a function, you have to replace every x with an y, as follows:
f(x) = 4y
then, replace f(x) with an x,
x = 4y
and now, isolate y,
x/4 = y
Finally, replace y whit h(x),
h(x) = 1/4x
please help me solve. The answer I have is incorrect which is 527.5
527.8 m³
1) Let's find out the Volume of the biggest cylinder then subtract from it the smaller one.
Big Cylinder Volume:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=\pi\cdot9^2\cdot3 \\ V=243\pi\approx763.4m^3 \end{gathered}[/tex]The Small one:
[tex]\begin{gathered} V=\pi\cdot5^2\cdot3 \\ V=75\pi m^3 \end{gathered}[/tex]Subtracting 75π from 243π we have:
V=243π -75π =168π approximately 527.7875658 to the nearest tenth: 527.8 m³
Patrick has a swimming pool that needs to be drained. His pool holds9,644.6 gallons of water and will need to drain completely in 8 hours.What is the change in the water level per hour for Patrick's swimmingpool? Round your answer to the nearest hundredth.
Explanation
We are asked to find the change in the water level per hour for Patrick's swimming
We have to use the formula
[tex]change\text{ in water level per hour=}\frac{Volume\text{ of water}}{Time\text{ taken to drain}}[/tex]Thus
[tex]change\text{ in water level per hour=}\frac{9644.6}{8}=1205.575\text{ gallons per hour}[/tex]Note: The rate will be negative because we are draining
Therefore, the change in water level will be -1205.58 gallons per hour
Can you help me with this? The approximate area of the circle is (Blank) square feet. (Use 22/7 as an approximation for pi) The approximate circumference of the circle is (Blank) feet. Use 22/7 as an approximation for pi
Let's begin by listing out the given information:
16x^2 + 56x + 49 Is this a special product? If yes, what type
Let's check if the given equation is a special product.
[tex]16x^2+56x+49[/tex]Let,
a = 1st term coefficien
b = 2nd term coefficient
c = constant
We get,
a = 16
b = 56
c = 49
Let's check, you can use this method to check if it is a perfect square binomial:
[tex]\begin{gathered} \text{ 2(}\sqrt[]{a}\text{ x }\sqrt[]{c})\text{ = b ;} \\ (a+c)^2\text{ if b is positive} \\ (a-c)^2\text{ if b is negative} \end{gathered}[/tex][tex]\begin{gathered} 2(\sqrt[]{16}\text{ x }\sqrt[]{49})\text{ = 56} \\ 2(4\text{ x 7) = 56 ; since b is positive, a and c are positive} \\ 2(28)\text{ = 56} \\ 56\text{ = 56} \end{gathered}[/tex]Therefore, the equation is a special product. It is a square of a binomial.
The answer is YES, it is a special product. It is a Square of a Binomial (x + y)².
Solve for v-2v-5v-17=25 Simplify your answer as much as possible
Given:
-2v-5v-17=25
To determine the value of v, we first add similar elements first:
[tex]\begin{gathered} -2v-5v-17=25 \\ -7v-17=25 \end{gathered}[/tex]Next, we add 17 to both sides:
[tex]\begin{gathered} -7v-17+17=25+17 \\ Simplify \\ -7v=42 \\ \frac{-7v}{-7}=\frac{42}{-7} \\ v=-6 \end{gathered}[/tex]Therefore, the value of v is -6.
A new song has gone viral on the Internet. The website hosting the song uses the function f(t)=500t^2 to represent the number of daily hits over time, where t is time in days. Use the function to predict the day on which the number of daily hits reaches 1,000,000. Show your work.
We will have the following:
[tex]\begin{gathered} 1000000=500t^2\Rightarrow t^2=2000 \\ \\ \Rightarrow t=\sqrt{2000}\Rightarrow t=20\sqrt{5} \\ \\ \Rightarrow t=44.72135955... \end{gathered}[/tex]So, on day 44 it will reach 1 000 000.
Be sure to fully show the system of equations for each problem and the process used to solve the system.You are starting an office-cleaning service. You decide to charge both large and small offices. You charge $55 for a small office and $85 for a large office. You clean 14 offices and make $920. How many small offices and how many large offices did you clean?
Given:
The charge for a small office = $55.
The charge for a large office = $ 85.
The total number of offices = 14.
The total amount = $ 920.
Required:
We need to find a number of small offices and large offices.
Explanation:
Let x be the number of the small office and y be the number of the large office.
The equation of the total number of offices.
[tex]x+y=14[/tex][tex]x=14-y[/tex]The equation of the total amount.
[tex]55x+85y=920[/tex]Substitute x =14-y in the equation.
[tex]55(14-y)+85y=920[/tex][tex]55\times14-55y+85y=920[/tex][tex]770+30y=920[/tex]Subtract 770 from both sides of the equation.
[tex]770+30y-770=920-770[/tex][tex]30y=150[/tex]Divide both sides by 30.
[tex]\frac{30y}{30}=\frac{150}{30}[/tex][tex]y=5[/tex][tex]Substitute\text{ y=5 in the equation x=14-y.}[/tex][tex]x=14-5[/tex][tex]x=9[/tex]Final answer:
The equations are
[tex]x+y=14[/tex][tex]55x+85y=920[/tex]The number of small offices are 9.
The number of large offices are 5.
Select all statements that must be true.
(Select all that apply)
Students selecting B are likely mistaking the range for
the IQR. Students selecting C are likely mistaking the
median for the IQR. Students selecting D are likely
mistaking the mean for the median. It may be possible
that the mean is 3.6 goals per game, but cannot be
determined from the box plot alone. Students selecting
F are likely mistaking Q1 for the minimum.
A. The interquartile range (IQR) is 1.2 goals per game.
B. The interquartile range (IQR) is 3.2 goals per game.
C. The interquartile range (IQR) is 3.6 goals per game.
The average goals scored per game are calculated for
20 soccer tournaments. The 20 averages are used to
create this box plot.
O O OOO
D. The mean is 3.6 goals per game.
E. The median is 3.6 goals per game.
E The minimum is 2.8 goals per game.
H
G. The maximum is 5.6 goals per game.
2
2.4 2.8 3.2 3.6
4
4.4
4.8
5.2 5.6
6
Average Number of Goals per
Game
The maximum = 5.6 goals per game
median = 3.6 goals per game
Interquartile range (IQR ) = 1.2 goals per games
Explanation:To solve this question, we need an illustration that identifies the part of the box and whiskers plot:
The minimum on the box and whiskers = 2.4 goals per game
The maximum = 5.6 goals per game
The median = the line in between the box
median = M on the image
median = 3.6 goals per game
upper quartile = Q3 = 4
lower quartile = Q1 = 2.8
The interquartile range = IQR
[tex]\begin{gathered} \text{IQR = Q}_3-Q_1 \\ \text{IQR = }4\text{ - 2.8} \\ \text{IQR = 1.2} \end{gathered}[/tex]Interquartile range (IQR ) = 1.2 goals per games
[tex]\begin{gathered} \text{Mean = average of the data set} \\ \text{Mean = }\frac{su\text{m of the numbers}}{nu\text{mber of the data set}} \\ \text{Mean = }\frac{2.4\text{ + }2.8+3.6+4+5.6}{5} \\ \text{Mean = 18.4/5} \\ \text{Mean = 3.68} \end{gathered}[/tex]The mean is 3.68 goals per game
What is the volume of this cone? Use 3.14 and round your answer to the nearest hundredth. 38 mm cubic millimeters
ANSWER
[tex]V=7179.09\operatorname{mm}[/tex]EXPLANATION
We are given the height of the cone as 19 mm and the diameter of its base as 38 mm.
The volume of a cone is given as:
[tex]V=\frac{1}{3}\pi\cdot r^2h[/tex]where r =radius; h = height
The diameter of a circle (the base of a cone) is twice the radius. Therefore:
[tex]\begin{gathered} D=2r \\ r=\frac{D}{2} \\ r=\frac{38}{2} \\ r=19\operatorname{mm} \end{gathered}[/tex]Therefore, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot19^2\cdot19 \\ V=7179.09\operatorname{mm}^3 \end{gathered}[/tex]put the following functions in order for smallest maxium to largest maxium
How many kg of water are in a 132 kg person ?
Answer:
[tex]88kg\text{ of water}[/tex]Explanation:
Here, we want to get the number of kg of water in a 132 kg person
From the question, there is a direct variation between kg of water in the human body and the mass of the body
Let the mass be m and the amount of water be w
By direct variation, with k as the proportionality constant, we have it that:
[tex]w\text{ = }km[/tex]From the question, a 72 kg mass boy has 48 kg of water
Mathematically, we have it that:
[tex]\begin{gathered} 48\text{ = k }\times72 \\ k\text{ = }\frac{48}{72} \\ \end{gathered}[/tex]Now, we want to get the kg of water in a 132 kg person
What we have to do here is to have k as 48/72 and solve for w
Mathematically, we have that as:
[tex]\begin{gathered} w\text{ = }\frac{48}{72}\times132 \\ \\ w\text{ = 88 }kg \end{gathered}[/tex]can you help pls with
Answer:
C. 3.5=3.50
Explanation:
Given the statements below:
[tex]\begin{gathered} A.$0.43>0.5$ \\ B.$0.65<0.56$ \\ C.3.5=3.50 \\ D$.2.45>2.54$ \\ E.$0.4<0.04$ \end{gathered}[/tex]The only true statement out of the given options is:
[tex]3.5=3.50[/tex]The correct choice is C.
State if the three numbers can be the measures of the ustedes of a triangle. 12, 18, 9
State if the three numbers can be the measures of the ustedes of a triangle.
12, 18, 9
Remember that
The triangle inequality theorem, states that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
so
12+9 > 18
21 > 18 -----> is true
You only need to see that the two smaller sides are greater than the largest side
therefore
the answer is
Yes, the three numbers can be the measures of the ustedes of a triangleAccording to psychologist IQs are normally distributed with a mean of 100 and a standard deviation of 19. What’s the percentage of the population has IQs above 154?
In order to solve this problem, we will calculate the z-score of the given data.
To do this, we use the formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]We plug in the given data:
[tex]z=\frac{154-100}{19}\approx2.8421[/tex]With this z-score, we can consult a z-score probability table or use an online resource. However, this will give us
[tex]P(z<2.8421)[/tex]but we are interested in itbeing greater than it, so we must calculate
[tex]1-P(z<2.8421)=1-0.99776=0.00224[/tex]So, the percentage of the population that has an IQ above 154 is 0.224%.
Use the number line to answer the question. Each tick represents 1.Which point is located at 2?PQSnone of the above
Given that each tick represents 1. The numbers on the right of 0 are positiv and on the left of 0 are negative. SInce 2 is positive, 2 lies on the right side of 0.
Since each tick represents 1, the first tick represents 0+1 = 1.
Now, the second tick represents 0 + 2 = 2. The second tick on the right of 0 denoted as S.
The correct option is S.
convert the following fraction to a decimal 3 15/16 a 2,5472 b. 3.156 c. 3.0375 d. 4. 238
ANSWER:
3.9375
EXPLANATION:
Given:
[tex]3\frac{15}{16}[/tex]To convert this to decimal, first convert the fraction, 15/16 to decimal:
[tex]\frac{15}{16}=\text{ 0.9375}[/tex]Now add the 3 whole number to 0.9375:
[tex]3\text{ + 0.9375 = 3.9375}[/tex]Describe the vertical asymptote (s) and hole (s) for the graph of y = (x+2) (x+4)/ (x+4) (x+1)
Given:
[tex]y=\frac{(x+2)(x+4)}{(x+4)(x+1)}[/tex]Required:
We need tofnind the vertical asymptote(s) and hole (s) for the graph of the given function.
Explanation:
Vertical asymptotes can be found when the numerator of the function is equal to zero.
The numerator of the given function is (x+4)(x+1)
[tex](x+4)(x+1)=0[/tex][tex](x+4)=0\text{ or }(x+1)=0[/tex][tex]x=-4\text{ or x=-1}[/tex]The asymptote of the given function is either x =-4 or x =-1.
Recall that a hole exists on the graph of a rational function when both the numerator and denominator of the function are equal to zero.
The common factor of the given rational function
multiply and simplify 2/5 × -7/4
Answer:
[tex]\frac{2}{5}\times\frac{-7}{4}=\frac{-7}{10}[/tex]Explanation:
Given the expression:
[tex]\frac{2}{5}\times\frac{-7}{4}[/tex]This is the same thing as
[tex]\frac{2\times(-7)}{5\times4}[/tex]evaluating this, we have
[tex]\frac{-14}{20}[/tex]Simplifying this, we have
[tex]\frac{-7}{10}[/tex]on a coordinate plane triangle XYZ is rotated 90 degrees counterclockwise about the origin to form triangle XYZ which conclusion is always true
Given a 90° rotation of triangle XYZ, every segment will rotate 90°, meaning that each segment will form a right angle with the corresponding transformed segment.
Thereby, the correct answer is:
[tex]\bar{YZ}\perp\bar{Y^{\prime}Z^{\prime}}[/tex]Answer B
Calculate the area of the circle shown below.10 in Approximate Value_________Exact Value________(round your approximate answers to thehundredths)Circumference of the circle:_________ in?_________ in?
The radius of the circle is r=10 in.
The circumference of the circle is,
[tex]\begin{gathered} C=2\pi r \\ =2\pi\times10 \\ =20\pi \\ =62.83in \end{gathered}[/tex]Thus, the exact value of circumference is 20pi inches and the approximate value is 62.83 in.
You randomly select one card from a 52-card deck. Find the probability of selecting a black eight or a black king.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
We have only two black eights on the deck and two black kings on the deck, therefore, the amount of favourable outcomes is equal to their sum, which is 4. The total amount of possible outcomes are the amount of cards, 52. The probability of selecting a black eight or a black king is:
[tex]P=\frac{4}{52}=\frac{1}{13}[/tex]