There are 66.4 milliliters of acid in the solution
Explanation:The amount of the solution of acid and water = 357
Percentage composition of acid in the solution = 18.6%
Amount of acid in the solution = (18.6/100) x 357
Amount of acid in the solution = 66.402 milliliters
Amount of acid in the solution = 66.4 milliliters (to the nearest tenth)
There are 66.4 milliliters of acid in the solution
the 9th term of arithmetic sequence. Use the formula for 'an' to find 'a20', the 20th term of the sequence 7,3,-1,-5
We will find the value of the 20th term of the sequence 7, 3, -1, and -5.
We have the following sequence:
[tex]7,3,-1,-5[/tex]Finding the common differenceIf we have an arithmetic sequence here, we need to find the common difference for this sequence, and we can do that by finding the difference between the second term and the first term, the difference between the third term and the second term, and so on. If we obtain the same value for the common difference, we have an arithmetic sequence here.
Then we have:
[tex]\begin{gathered} d=3-7=-4 \\ \\ d=-1-3=-4 \\ \\ d=-5-(-1)=-5+1=-4 \end{gathered}[/tex]Then the common difference in this arithmetic sequence is d = -4.
Finding the formula for the arithmetic sequenceWe know that the explicit formula for an arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]For this case, we have that d = -4, and that the first term, a1 = 7. Then we have the formula for the arithmetic sequence:
[tex]a_n=7+(n-1)(-4)[/tex]Notice that we can expand this expression as follows:
[tex]\begin{gathered} a_n=7+(-4)(n)+(-4)(-1) \\ \\ a_n=7-4n+4 \\ \\ a_n=11-4n \\ \end{gathered}[/tex]Finding the 20th termThen to find the 20th term of the sequence, we have:
[tex]\begin{gathered} a_{20}=7+(20-1)(-4) \\ \\ a_{20}=7+(19)(-4) \\ \\ a_{20}=7-76=-69 \\ \\ a_{20}=-69 \end{gathered}[/tex]Therefore, in summary, we have that the value for the 20th term of the sequence 7, 3, -1, and -5 is -69.
,
HELP PLEASE will give BRAINLIEST!!! You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is
y = 3/2x +6. There is a tree in your yard at the point (6, 2). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the
tree from the zip line? Round your answer to the nearest tenth.
Answer:
Hello lovely. Assume that the attached graph represents your situation, with the red line representing the zip line and the blue dot representing the tree. The tree is at point (6, 2). You will need to choose a reference point to calculate the distance between the tree and the zip line. We'll use the point (0, 6), or the y intercept
To calculate the distance between two points, we use the formula d=√((x2 – x1)² + (y2 – y1)²).
Substitute
d=√((0 – 6)² + (6 – 2)²).
Simplify
d=√((-6)² + (4)²).
d=√(36 + 16).
d = √52
The distance is approximately equal to 7.2 feet
1. Write the equation of the line with a slope of -3 that passes through the point (1,9).y=3x + 12y=3x + 6y=-32 +6y=-3x+12
Answer:
y = -3x + 12
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be calculated as:
[tex]y-y_1=m(x-x_1)[/tex]So, replacing m by -3, and (x1, y1) by (1, 9), we get:
[tex]y-9=-3(x-1)[/tex]Finally, solving for y, we get:
[tex]\begin{gathered} y-9=-3x-3(-1) \\ y-9=-3x+3 \\ y-9+9=-3x+3+9 \\ y=-3x+12 \end{gathered}[/tex]Therefore, the answer is:
y = -3x + 12
You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 4 minutes and you record the data point of (12,y), what is the value of y? Use slope to justify your answer
Answer:
51
Step-by-step explanation:
so we can use the variable x for minutes & y for water level. (4,17) is what we start with. its asking after 12 minutes what is the water level, 4 x 3 is 12 so we would multiply 17 x 3 as well which is 51.
Write the equation of a line in point slope form that goes through the points (7,-5) and (3,8)
Write the equation of a line in point slope form that goes through the points (7,-5) and (3,8)
step 1
Find the slope
m=(8+5)/(3-7)
m=13/-4
m=-13/4
step 2
write the equation in point slope form
so
y-y1=m(x-x1)
we take the point (7,-5)
substitute
y+5=-(13/4)(x-7)If you take the point (3,8)
we have
y-8=-(13/4)(x-3)A population forms a normal distribution with a meanof μ = 85 and a standard deviation of o = 24. Foreach of the following samples, compute the z-score forthe sample mean.a. M=91 for n = 4 scoresb. M=91 for n = 9 scoresc. M=91 for n = 16 scoresd. M-91 for n = 36 scores
In this problem, we have a population with a normal distribution with:
• mean μ = 85,
,• standard deviation σ = 24.
We must compute the z-score for different samples.
The standard deviation of a sample with mean M and size n is:
[tex]σ_M=\frac{σ}{\sqrt{n}}.[/tex]The z-score of the sample is given by:
[tex]z(M,n)=\frac{M-\mu}{\sigma_M}=\sqrt{n}\cdot(\frac{M-\mu}{\sigma})[/tex]Using these formulas, we compute the z-score of each sample:
(a) M = 91, n = 4
[tex]z(91,4)=\sqrt{4}\cdot(\frac{91-85}{24})=0.5.[/tex](b) M = 91, n = 9
[tex]z(91,9)=\sqrt{9}\cdot(\frac{91-85}{24})=0.75.[/tex](c) M = 91, n = 16
[tex]z(91,16)=\sqrt{16}\cdot(\frac{91-85}{24})=1.[/tex](d) M = 91, n = 36
[tex]z(91,9)=\sqrt{36}\cdot(\frac{91-85}{24})=1.5.[/tex]Answera. z = 0.5
b. z = 0.75
c. z = 1
d. z = 1.5
Find a standard form of the equation for the circle with the following property
Solution:
Given:
[tex]Endpoints\text{ }(-7,5)\text{ and }(-5,-1)[/tex]To get the equation of the circle, the center of the circle and the radius are needed.
The center of the circle is the midpoint of the endpoints.
Using the midpoint formula;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} M=(\frac{-7+(-5)}{2},\frac{5+(-1)}{2}) \\ M=(\frac{-12}{2},\frac{4}{2}) \\ M=(-6,2) \end{gathered}[/tex]Hence, the coordinates of the center of the circle is (-6,2)
The length of the diameter can be gotten using the distance between two points formula;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \\ Hence, \\ d=\sqrt{(-5-(-7))^2+(-1-5)^2} \\ d=\sqrt{2^2+(-6)^2} \\ d=\sqrt{4+36} \\ d=\sqrt{40} \end{gathered}[/tex]The diameter is twice the radius. Hence, the radius is;
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{\sqrt{40}}{2}=\frac{2\sqrt{10}}{2} \\ r=\sqrt{10} \end{gathered}[/tex]Hence, the equation of the circle with center (-6,2)
[tex]with\text{ radius }\sqrt{10}[/tex]Using the standard form of the equation of a circle;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where: \\ (h,k)\text{ }is\text{ }the\text{ center} \\ r\text{ is the radius} \\ h=-6 \\ k=2 \\ r=\sqrt{10} \end{gathered}[/tex]Hence, the equation is;
[tex]\begin{gathered} (x-(-6))^2+(y-2)^2=(\sqrt{10})^2 \\ (x+6)^2+(y-2)^2=10 \end{gathered}[/tex]Therefore, the equation of the circle is;
[tex](x+6)^{2}+(y-2)^{2}=10[/tex]
If L = 4 inches and KL = 7 inches, what is the length of the diameter JK? Round your answer to at least the nearest hundredth of an inch (2 decimal places).
We have a right triangle and two sides we will use the Pythagorean theorem in order to find the missing side
[tex]c^2=a^2+b^2[/tex]a=7 in
b= 4 in
c=JK
we substitute the values
[tex]JK=\sqrt[]{7^2+4^2}[/tex][tex]JK=8.06[/tex]translating words into algebraic symbols its not -70 or -7
translating words into algebraic symbols
a number x = x
decreased by seventy = -7
y= x-70
___________________
Answer
x-70
Carlos is adding insulation to a room he just finished framing in his home. The room is 16ft. by 12ft., and the ceilings are 9ft. tall. There are two windows in the room measuring 5ft. by 6ft. each. How many square feet of insulation does Carlos need?
Solution
Now
[tex]A=2(16\times12)+2(16\times9)+2(9\times12)-2(5\times6)[/tex][tex]828ft^2[/tex]square feet of insulation Carlos need is
[tex]828ft^2[/tex]Use the positions of the numbers on the number line to compare them.Select the two true inequalities.A. 3/4 < 4/5B. 0.85 > 4/5C. 3/4 > 4/5D. 0.85 < 4/5
Answer:
Explanation:
Given:
0.85,4/5, 3/4
To easily compare the given numbers, we simplify each number first and plot them on the number line:
Therefore, the two true inequalities are:
[tex]\frac{3}{4}<\frac{4}{5}[/tex]and
[tex]0.85>\frac{4}{5}[/tex]5. Jeannette has $5 and $10 bills in her wallet. The number of fives iseight more than five times the number of tens. Let t represent theNumber of tens. Write an expression for the number of fives.
The number of fives is eight more than five times the number of tens.
Therefore,
[tex]F=5\cdot T+8[/tex]where F represents the number of fives and T the number of tens
Please step-by-step help me how much of a circle is shaded
The given data is ratio from the the total are of circle is 1 .
let the shaded area is x then:
All area is equal to one.
[tex]\begin{gathered} \frac{1}{2}+\frac{2}{9}+x=1 \\ \frac{9+4}{18}+x=1 \\ \frac{13}{18}+x=1 \\ x=1-\frac{13}{18} \\ x=\frac{18-13}{18} \\ x=\frac{5}{18} \end{gathered}[/tex]So area of shaded region is
[tex]\frac{5}{18}[/tex]Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Problem
Find the marked price and the rate of discount for a camcorder whose price has been reduced by 95$ and whose sale price is 255$.
Solution
For this case we can find the real price with this operation:
95+265= 360
And the rate of discount can be founded as:
(95/265)*100= 35.85%
Rounded to the nearest percent would be 36%
Need help with my math please..
Answer:
i can't read this very well
Find a polynomial function with real coefficients that has the given zeros
1 -√3i, 2
Answer:
[tex]x^3-4x^2+8x-8[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(x-(1-\sqrt{3} i)(x-(1+\sqrt{3} i)(x-2)=\\\\(x^2-(1-\sqrt{3} i)x-(1+\sqrt{3} i)x+(1-\sqrt{3} i)(1+\sqrt{3} i))(x-2)=\\\\(x^2-x+\sqrt{3} i-x-\sqrt{3} i+1-(\sqrt{3} i)^2)(x-2)=\\\\(x^2-2x-3\cdot(-1))(x-2)=\\\\(x^2-2x+4)(x-2)=\\\\x^3-2x^2+4x-2x^2+4x-8=\\\\x^3-4x^2+8x-8[/tex]
Which statements are true?Select all that apply.A.The slope of AC is equal to the slope of BC.B.The slope of AC is equal to the slope of BD.C.The slope of AC is equal to the slope of line t.D.ECThe slope of line t is equal toAEE.FBThe slope of line t is equal toFDF.The slope of line t is equal to AB
Line t, segments AC, BC and BD are colinear, that is, all of them are in the same line. Then, the true statements are
A, B, and C
Find the 11th term of the arithmetic sequence -5x- 1, -8x + 4, -11 x+ 9, ...
Recall that an arithmetic sequence is a sequence in which the next term is obtained by adding a constant term to the previous one. Let us consider a1 = -5x-1 as the first term and let d be the constant term that is added to get the next term of the sequence. Using this, we get that
[tex]a_2=a_1+d[/tex]so if we replace the values, we get that
[tex]-8x+4=-5x-1+d[/tex]so, by adding 5x+1 on both sides, we get
[tex]d=-8x+4+5x+1\text{ =(-8+5)x+5=-3x+5}[/tex]To check if this value of d is correct, lets add d to a2. We should get a3.
Note that
[tex]a_2+d=-8x+4+(-3x+5)=-11x+9=a_3[/tex]so the value of d is indeed correct.
Now, note the following
[tex]a_3=a_2+d=(a_1+d)+d=a_1+2d=a_1+d\cdot(3-1)[/tex]This suggest the following formula
[tex]a_n=a_1+d\cdot(n-1)[/tex]the question is asking for the 11th term of the sequence, that is, to replace the value of n=11 in this equation, so we get
[tex]a_{11}=a_1+d\cdot(10)=-5x-1+10\cdot(-3x+5)\text{ =-5x-1-30x+50 = -35x+49}[/tex]so the 11th term of the sequence is -35x+49
The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. Find the probability of wearing a seat belt, given that the driver did not survive a car accident. Part 1: The probability as a decimal is _ (Round to 3 decimal places as needed.) Part 2: The probability as a fraction is _
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
The table shows the outcome of car accidents by whether or not the driver wearing a seat belt.
Let's call:
A = The event of the driver wearing a seat belt in a car accident.
B = The event of the driver dying in a car accident
The conditional probability is calculated as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]The conditional probability stated in the formula is that for the driver wearing a seat belt knowing he did not survive the car accident.
The numerator of the formula is the probability of both events occurring, i.e., the driver wore a seat belt and died. The denominator is the simple probability that the driver died in a car accident.
From the table, we can intersect the first column and the second row to find the number of outcomes where both events occurred. The probability of A ∩ B is:
[tex]P(A\cap B)=\frac{511}{583,470}[/tex]The probability of B is:
[tex]P(B)=\frac{2217}{583,470}[/tex]The required probability is:
[tex]P(A|B)=\frac{\frac{511}{583,470}}{\frac{2217}{583,470}}[/tex]Simplifying the common denominators:
[tex]P(A|B)=\frac{511}{2217}=0.230[/tex]Find the solution(s) to the system of equations represented in the graph.0, −2) and (2, 0) (0, −2) and (−2, 0) (0, 2) and (2, 0) (0, 2) and (−2, 0)
Solution
The solution is the point of intersection.
Therefore, the answer is
[tex](0,2)\text{ and }(-2,0)[/tex]cube A has a volume of 125 cubic inches The Edge length of cube B measures 4.8 inches. which group is larger and why?select the corrects responses1. Cube A, because it's volume is greater than the volume of cube B 2. Cube A, because its surface area is greater than the volume of cube B 3. Cube B, because it's volume is greater than the volume of cube A4. Cube B, because its side length is greater than the side length of cube A
Answer:
1. Cube A, because it's volume is greater than the volume of cube B
Explanation:
Cube A
Volume = 125 cubic inches
[tex]\begin{gathered} \text{Volume}=s^3(s=\text{side length)} \\ 125=s^3 \\ s^3=125 \\ s^3=5^3 \\ s=5\text{ inches} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \text{Surface Area=}6s^2 \\ =6(5)^2 \\ =6\times25 \\ =150\text{ square inches} \end{gathered}[/tex]Cube B
The edge length, s = 4.8 inches.
[tex]\begin{gathered} \text{Volume}=4.8^3=110.592\text{ cubic inches} \\ \text{Surface Area=}6(4.8)^2=138.24\text{ cubic inches} \end{gathered}[/tex]We see that Cube A is the larger group because it's volume is greater than the volume of cube B.
what is the slope of the line that passes through the points of (5,3) (5.-9)
Answer:
undefined
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-9 - 3)/(5 - 5)
slope = -12/0
Since the slope calculation involves division by zero, this line has undefined slope. The two points have the same x-coordinate, so the line is vertical. The slope of a vertical line is undefined.
Andrew says the scale factor used was 3\2. Annie says the scale factor used was 2\3.Which student is correct and why?
Answer:
Annie is right, beause the coordinates of the points A'B'C' are 2/3 of the coodinates of the points ABC
and the size of the triangle A'B'C' is 2/3 of the size of the triangle ABC
for example:
Side AC lenght is 6 units and A'C' is 4
To go from 6 to 4, the factor must be 2/3
Hi, could I have some help answering this question in the picture attached?simplify the question
Expand and collect like terms:
[tex]\begin{gathered} =\text{ }7s^{\frac{7}{4}}\times t^{\frac{-5}{3}}\times-6s^{\frac{-11}{4}}\times t^{\frac{7}{3}} \\ =\text{ }7\times s^{\frac{7}{4}}\times-6\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \\ =\text{ 7 }\times-6\text{ }\times\text{ }s^{\frac{7}{4}}\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \\ =\text{ -42}\times\text{ }s^{\frac{7}{4}}\times s^{\frac{-11}{4}}\times t^{\frac{-5}{3}}\times t^{\frac{7}{3}} \end{gathered}[/tex]Bring the exponents having same base together:
[tex]\begin{gathered} \text{The multiplication betwe}en\text{ same base becomes addition } \\ \text{when the exponents are brought together} \\ =-42\text{ }\times\text{ }s^{\frac{7}{4}-\frac{11}{4}}\times t^{\frac{-5}{3}+\frac{7}{3}} \\ =\text{ -42 }\times s^{\frac{7-11}{4}}\times t^{\frac{-5+7}{3}} \\ =\text{ -42 }\times s^{\frac{-4}{4}}\times t^{\frac{2}{3}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ -42 }\times s^{\frac{-4}{4}}\times t^{\frac{2}{3}} \\ =\text{ -42 }\times s^{-1}\times t^{\frac{2}{3}} \\ =\text{ -42}s^{-1}t^{\frac{2}{3}} \end{gathered}[/tex]shron spent 1 1/4 hours reading her book report and 2 2/5 hours doing her other homework. how much longer did sharon spent doing her homework than reading her book report
sharon spent 23/20 hour doing her homework than reading.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Sharon spent reading the book = [tex]1 \frac{1}{4}[/tex] = 5/4 hours
= 25/20 hours
Sharon spend doing homework = [tex]2 \frac{2}{5}[/tex] = 12/5 hours
= 48/20 hours
So, the difference between both activities
= 48/20- 25/20
= 23/20
Hence, sharon spent 23/20 hour doing her homework than reading.
Learn more about fraction here:
https://brainly.com/question/10354322
#SPJ1
You need a shelf for a small space in your house, so you make a measurement with your meter stick and head to the store. Once there, you find that the dimension of the shelves you want is given in cm.If your space measured 0.9 m, and the shelves at the store measure 30 cm, answer the following questions:1) How many meters wide is the shelf you want to buy?
We will have the following:
[tex]0.9m=90cm[/tex]So, the number of shelves you need is 3.
Thus, the shelves you can buy are 0.3 m long each.
The circumference of a circle is 278.71m. What is the approximate area of the circle? Use 3.14 for pi. Explain how the area of a circle changes when the circumference of a circle changes ( round the final answer to the nearest whole number as needed , round all the intermediate values to the nearest thousandth as needed )
The circumference of a circle can be found through the formula:
[tex]C=2\cdot\pi\cdot r[/tex]clear the equation for the radius
[tex]r=\frac{C}{2\pi}[/tex]find the radius of the circumference
[tex]\begin{gathered} r=\frac{278.71}{2\pi} \\ r\approx44.358 \end{gathered}[/tex]find the area of the circle using the formula
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot(44.358)^2 \\ A\approx6181 \end{gathered}[/tex]The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.9 ppm and standard deviation 1.8 ppm. 39 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
ANSWER:
a. 9.9, 1.8
b. 9.9, 0.2882
c. 0.5239
d. 0.6368
e. No
f.
Q1 = 9.7069
Q3 = 10.0931
IQR = 0.3862
STEP-BY-STEP EXPLANATION:
a.
X ~ N (9.9, 1.8)
b.
x ~ N (9.9, 1.8/√39)
x ~ N (9.9, 0.2882)
c.
P(X > 9.8)
We calculate the probability as follows:
[tex]\begin{gathered} P\left(X>9.8\right)=1-p\left(\frac{X-9.9}{1.8}<\frac{9.8-9.9}{1.8}\right) \\ \\ P\left(X>9.8\right)=1-p(z<-0.06) \\ \\ P\left(X>9.8\right)=1-0.4761 \\ \\ P\left(X>9.8\right)=0.5239 \end{gathered}[/tex]d.
p (x > 9.8)
We calculate the probability as follows:
[tex]\begin{gathered} P\left(x>9.8\right)=1-p\left(\frac{X-9.9}{\frac{1.8}{\sqrt{39}}}<\frac{9.8-9.9}{\frac{1.8}{\sqrt{39}}}\right) \\ \\ P\left(x>9.8\right)=1-p(z<-0.35) \\ \\ P\left(x>9.8\right)=1-0.3632 \\ \\ P\left(x>9.8\right)=0.6368 \end{gathered}[/tex]e.
No, you don't need to make the assumption
f.
Q1 = 0.25
In this case the value of z = 0.25, so we look for the closest value in the normal table, like this:
Thanks to this, we make the following equation:
[tex]\begin{gathered} -0.67=\frac{x-9.9}{\frac{1.8}{\sqrt{35}}} \\ \\ x-9.9=-0.19311 \\ \\ x=-0.1931+9.9 \\ \\ x=9.7069 \\ \\ Q_1=9.7069 \end{gathered}[/tex]Q3 = 0.75
In this case the value of z = 0.75, so we look for the closest value in the normal table, like this:
Therefore:
[tex]\begin{gathered} -0.67=\frac{x-9.9}{\frac{1.8}{\sqrt{39}}} \\ \\ x-9.9=0.1931 \\ \\ x=0.1931+9.9 \\ \\ x=10.0931 \\ \\ Q_3=10.0931-9.7069 \end{gathered}[/tex]Therefore, the interquartile range would be:
[tex]\begin{gathered} IQR=Q_3-Q_1 \\ \\ IQR=10.0931-9.7069 \\ \\ IQR=0.3862 \end{gathered}[/tex]Calculate the five-number summary of the given data. Use the approximation method.19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Answer:
Explanation:
Given the data:
19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Step 1: Write in an order (we are writing in an ascending order here)
2, 2, 2, 4, 8, 8, 10, 11, 16, 18, 19, 20, 23, 25,
Find any value of x that makes the equation x + 100 = x - 100 true.
Since the sides are the same, this problem is unsolvable