The measuring rule shows lines graded between each unit.
Each unit has four lines between them which means each line is a quarter, or 1/4 or 0.25 of each unit.
When the ruler indicates 0.5, that is shown as two quarters, or one half (that is 1/2).
Therefore when the ruler indicates
[tex]\begin{gathered} 1\frac{7}{8} \\ \text{That can be broken down into } \\ 1+\frac{2}{8}+\frac{2}{8}+\frac{2}{8}+\frac{1}{8} \\ \text{Note that }\frac{2}{8}\text{ is equivalent to }\frac{1}{4} \\ \text{Also }\frac{1}{4}\text{ is equivalent to 0.25} \\ \frac{1}{8}\text{ is half of }\frac{1}{4},\text{ and that is equivalent to half of 0.25} \\ \text{Therefore, we now have} \\ 1+0.25+0.25+0.25+0.125 \\ =1.875 \end{gathered}[/tex]The correct answer is 1.875
how do i isolate F in the equation C= 5 over 9 (F - 32)
According to the given data we have the following:
[tex]C=\frac{5}{9}(f-32)[/tex]In order to isolate F in the equation we would make the following:
First we would have the following property:
[tex]\frac{a}{b}=\frac{m}{n}=a\cdot n=b\cdot m[/tex]Therefore 9C=5f-160
9C+160=5f
So:
[tex]\begin{gathered} \frac{9C\text{ + 160}}{5}=f \\ \frac{9}{5}C+32=f \end{gathered}[/tex]2. Write an expression for the perimeter of a rectangle with a length of(3x2 + x + 2) and a width of (-22 – 5x + 1).O 4248x 7.60 4224x + 34x28x + 6O 2x24x + 3
You have that the perimeter of the rectangle is given by the following formula:
[tex]P=2l\text{ + 2w}[/tex]l: length of the rectangle
w: width of the rectangle
[tex]\begin{gathered} l=3x^2+x+2 \\ w=-x^2-5x+1 \end{gathered}[/tex]Then, you replace the pevious expression for l and w in the formula for the perimeter, just as follow:
[tex]\begin{gathered} P=2(3x^2+x+2)+2(-x^2-5x+1) \\ P=2(3x^2)+2(x)+2(2)+2(-x^2)+2(-5x)+2(1) \\ P=6x^2+2x+4-2x^2-10x+2 \\ P=4x^2-8x+6 \end{gathered}[/tex]Hence, the perimeter of the rectangle is P = 4x2 - 8x + 6
identify the distances in the other two polygons that correspond to DB and AC
You have to determine the distance of the diagonals of the polygons.
Asuming each square of the grid corresponds to one unit, to determine said distances you have to count the squares.
For the second polygon the diagonals are HF= 6 and GE= 9
For the third polygon the diagonals are LJ=2 and KI= 3
A teacher asks her students to use the Multiplication Property ofX-4.4 = 3.4. Courtney writes x = 4.100 = 3.100. Have bothEquality to write an equation equivalent to x 4 = 3. Alondra writesstudents followed the teacher's instructions? Explain your reasoning.
we have the equation
[tex]\frac{x}{4}=3[/tex]Alondra
Multiply by 4 both sides (property equality of multiplication)
so
[tex]\begin{gathered} \frac{x}{4}\cdot4=3\cdot4 \\ x=12 \end{gathered}[/tex]Courtney
Multiply by 100 both sides (property equality of multiplication)
[tex]\begin{gathered} \frac{x}{4}\cdot100=3\cdot100 \\ 25x=300 \end{gathered}[/tex]therefore
Both followed the teacher's guidelines, but by multiplying by 4, Alondra was able to solve the equation, while Courtney had to apply additional steps.
Please Help. Functions and Relations. A power company calculates a persons monthly bill from the number of kilowatt- hours (kWh), x, used. how much is the bill for a person who used 600 kWh in a month?
ANSWER:
B. $80
EXPLANATION:
[tex]b(x)=\begin{cases}0.15x,{x\leq400} \\ 0.10(x-400)+60,x>400{}\end{cases}[/tex]We'll use the below function to determine how much is the bill for a person who uses 600 kWh in a month;
[tex]\begin{gathered} b(x)=0.10(x-400)+60 \\ b(600)=0.10(600-400)+60 \\ =0.10(200)+60 \\ =20+60 \\ =\text{\$}80 \end{gathered}[/tex]So the bill is $80
I need to solve the following system of equations and enter my answers as an ordered pair the equations are 3x + y equals -10 and 2y + 8 equals -4x
a map has a scale on it which 3in represents 50 miles use information to match each map distance on the left to the number of miles to distant represent on the right
It is given that the scale used in the map is,
[tex]3\text{ in}\equiv50\text{ miles}[/tex]For 9 inches,
[tex]9\text{ inches=3}\times(\text{3 inches)}\equiv\text{3}\times(\text{50 miles)}=150\text{ miles}[/tex]Thus, a distance of 9 inches on the map corresponds to 150 miles in actual.
For 15 inches,
[tex]15\text{ inches=5}\times(\text{3 inches)}\equiv5\times(\text{50 miles)}=250\text{ miles}[/tex]Thus, a distance of 15 inches on the map corresponds to 250 miles in actual.
For 21 inches,
[tex]21\text{ inches=7}\times(\text{3 inches)}\equiv7\times(\text{50 miles)}=350\text{ miles}[/tex]Thus, a distance of 21 inches on the map corresponds to 350 miles in actual.
The harris family and the carter family each used their sprinklers last summer. The water output rate for the Harris family's sprinkler was 25 L per hour. The water output rate for the Carter family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1075 L. How long was each sprinkler used?
Let Harris family used their sprinkler for x hours and Carter family used their sprinkler for y hours.
Then the equation for total time of sprinkler use is,
[tex]\begin{gathered} x+y=55 \\ y=55-x \end{gathered}[/tex]Determine the equation for total water output from both the sprinkler.
[tex]\begin{gathered} 25x+15y=1075 \\ 5x+3y=215 \end{gathered}[/tex]Substitute 55-x for y in the equation to eliminate the y terms.
[tex]\begin{gathered} 5x+3(55-x)=215 \\ 5x+165-3x=215 \\ 2x=50 \\ x=25 \end{gathered}[/tex]Substitute 25 for x in the equation y=55-x to obtain the value of y.
[tex]\begin{gathered} y=55-25 \\ =30 \end{gathered}[/tex]So Harris family used sprinkler for 25 hours and Carter family used sprinkler for 30 hours.
Can I Plss get some help on my homework I got stuck es
Hello there. To solve this question, we'll have to remember some properties about mean and standard deviation.
Given the table with the calories of each pizza type.
We have to determine why the standard deviation is 87.6 and understand what does it mean in context.
First, the mean of the values were calculated in question 8, that is the arithmetic mean of the values.
Adding all calories and dividing it by the number of values, we get
[tex]\dfrac{168+181+165+177+321+380+309+313+157}{9}=\frac{2171}{9}\approx241.2[/tex]Okay. Now, we find the variance of the set by using the formula:
[tex]Var(x)=\sum_{i=1}^n\dfrac{(x_i-\mu)^2}{n}[/tex]In which we get
[tex]Var(x)=\dfrac{(168-241.2)^2+(181-241.2)^2+\cdots+(157-241.2)^2}{9}=7673.2[/tex]And the standard deviation is the square root of the variance, hence
[tex]\sigma=\sqrt{Var(x)}=\sqrt{7673.2}\approx87.6[/tex]In statistics, the standard deviation is a measure of how are the values getting away from the meanO, that is the point in the middle of the distribution:
This is the answer we're looking for.
For number eleven, suppose the new pizza has x calories.
We'll have a change in the mean, now being
[tex]\mu=\dfrac{2171+x}{10}[/tex]And the variance will be
[tex]Var(x)=\sum_{i=1}^n\dfrac{(x_i-\mu)^2}{10}=\dfrac{\left(168-\dfrac{2171+x}{10}\right)^2+\left(181-\dfrac{2171+x}{10}\right)^2+\left(177-\dfrac{2171+x}{10}\right)^2+\left(157-\dfrac{2171+x}{10}\right)^2+\left(321-\dfrac{2171+x}{10}\right)^2+\left(309-\dfrac{2171+x}{10}\right)^2+\left(380-\dfrac{2171+x}{10}\right)^2+\left(313-\dfrac{2171+x}{10}\right)^2+\left(165-\dfrac{2171+x}{10}\right)^2+\left(x-\dfrac{2171+x}{10}\right)^2}{10}[/tex]Consider taking x to be closer to the mean, that is
[tex]x\approx241.2[/tex]So the mean would be
[tex]\dfrac{2171+241.2}{10}\approx241.2[/tex]Won't change at all
And the difference between the value would be identically zero
Hence the variance will become smaller, making the standard deviation (the square root of it), smaller as well = 82.58
use the graph of y=-x/3 -1 determine which of the ordered pairs of the solution to the equation select all correct answers
Given:
[tex]y=-\frac{x}{3}-1[/tex]We have the graph below:
To determine the correct ordered pairs, let's solve for each of them.
a) (x, y) ==> (0, -1)
From the equation, substitute 0 for x and -1 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -1=-\frac{0}{3}-1 \\ \\ -1=0-1 \\ \\ -1=-1 \\ \\ \text{Therefore (0, -1) is a solution} \end{gathered}[/tex]b) (x, y) ==> (3, -2)
Substitute 3 for x and -2 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -2=-\frac{3}{3}-1 \\ \\ -2=-1-1 \\ \\ -2=-2 \\ \\ (3,\text{ -2) is a solution} \end{gathered}[/tex]c) (x, y) ==> (3, -5)
Substitute 3 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{3}{3}-1 \\ \\ -5=-1-1 \\ \\ -5=-2 \\ \\ (3,\text{ -5) is not a solution} \end{gathered}[/tex]d) (0, -5)
Substitute 0 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{0}{3}-1 \\ \\ -5=0-1 \\ \\ -5=-1 \\ \\ (0,\text{ -5) is not a solution} \end{gathered}[/tex]e) (x, y) ==> (-3, 0)
Substitute -3 for x and 0 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ 0=-\frac{-3}{3}-1 \\ \\ 0=1-1 \\ \\ 0=0 \\ \\ \text{The ordered pair (-3, 0) is a solution} \end{gathered}[/tex]ANSWER:
(0, -1)
(3, -2)
(-3, 0)
enter the ratio as a fraction in lowest terms 4ft to 82in
Answer
(4 ft/82 in) = (24/41)
Explanation
To answer this, we first need to note that
1 foot = 12 inches
So,
4 feet = 4 × 12 = 48 inches
So,
4 ft to 82 inches
= 48 inches to 82 inches
Dividing both sides by 2, we have
48 inches to 82 inches
= 24 inches to 41 inches.
In fraction form,
(4 ft/82 in) = (24/41)
Hope this Helps!!!
A person invested $7, 900 in an account growing at a rate allowing the money todouble every 8 years. How much money would be in the account after 5 years, to thenearest dollar?
Given,
The principal amount is $7900.
The time period is 8 years.
The amount of the investment is double of the principal.
Required:
The money would be in the account after 5 years, to the nearest dollar.
The Amount is calculated as:
[tex]\begin{gathered} Amount\text{ = }\frac{Principal\times rate\times time}{100}+principal \\ Amount=(\frac{\text{rate}\times\text{t}\imaginaryI\text{me}}{\text{100}}\text{+1\rparen pr}\imaginaryI\text{nc}\imaginaryI\text{pal} \end{gathered}[/tex]Substituting the value in the above formula then,
[tex]\begin{gathered} 15800=(\frac{\text{rate}\times8}{\text{100}}\text{+1\rparen7900} \\ 2=\frac{rate\times8}{100}+1 \\ 1=rate\times\frac{8}{100} \\ rate=\frac{100}{8} \\ Rate=12.5\text{ \%} \end{gathered}[/tex]The amount in the account after 5 years is:
[tex]\begin{gathered} Amount\text{ =7900\lparen}\frac{5\times12.5}{100}+1) \\ =7900\times\frac{162.5}{100} \\ =12837.5 \end{gathered}[/tex]Hence, money would be in the account after 5 years is $12837.5
Find the value of the expression below.log4 3 + log4 8 - log4 6A.1B.3C.0D.2
Given:
[tex]log_43+log_48-log_46[/tex]To Determine: The value of the given expression
Solution
Let us apply the logarithm rule below
[tex]\begin{gathered} logA+logB=log(A\times B) \\ So \\ log_43+log_48=log_4(3\times8)=log_424 \\ log_43+log_48-log_46=log_424-log_46 \end{gathered}[/tex]Applying the rule below again
[tex]\begin{gathered} logA-logB=log(A\div B) \\ So, \\ log_424-log_46=log_4(24\div6)=log_44 \end{gathered}[/tex]And finally applying the rule below
[tex]\begin{gathered} log_aa=1 \\ Then \\ log_44=1 \end{gathered}[/tex]Hence, the solution of the given expression is 1, OPTION A
so im working on mixed properties homeworkand i just need help on it. so one question is determine the algebraic property shown so i need to know the property of 7*2 and 2*7
Recall that we are given the numbers 2*7 and 7*2. By a fact, we have that
[tex]7\cdot2\text{ =2}\cdot7[/tex]Note that in both cases, we are multiplying numbers 2 and 7, but what is changed it the order in which we do so. On the expression on the left we are multiplying 7 times 2, and on the expression on the expression on the right we are multiplying 2 times 7. This two expressions are equal due to the conmutative property of the multiplication of integers.
which square root is a whole number ?
Let's find the square root of all to find which is a whole number
√254 = 15.937
√255 =15.967
√256 =16
Hence √256 is a whole number
The correct option is C.
Is the inequality always, sometimes, or never true?5x - 6<5(x - 5)Choose the correct answer below.Sometimes trueNever trueAlways true
In order to avaliate the inequatily, let's first expand the parenthesis in the right side:
[tex]5x-6<5x-25[/tex]We can subtract 5x from both sides of the inequality:
[tex]-6<-25[/tex]-6 is not lesser than -25, and any value of x we use will not change the final inequality, so this inequality is NEVER TRUE.
5. If AKLJ - AVWU, find the value of x.
The triangles are similar according to the question. Therefore, the following ratio can be formed
[tex]\begin{gathered} \frac{25}{20}=\frac{4x-23}{2x+2} \\ \text{cross multiply} \\ 25(2x+2)=20(4x-23) \\ 50x+50=80x-460 \\ 50x-80x=-460-50 \\ -30x=-510 \\ x=\frac{-510}{-30} \\ x=17 \end{gathered}[/tex]If PR = 10 and PQ = 4, then QR =
PR = 10 and PQ = 4 QR
QR is the difference between PR and PQ . Hence
QR = 10 - 4
= 6
1) write each mixed number as a decimal 2 2/52) write each decimal as a fraction in simplest form: 0.5
1) 2.4 2) 1/2
First, let's rewrite:
[tex]2\frac{2}{5}[/tex]We would convert the fraction to decimal and add the outcome to the whole number:
[tex]\begin{gathered} \frac{2}{5}\text{ = 0.4} \\ \text{whole number = 2} \\ 2\frac{2}{5}\text{ = 2 + }\frac{2}{5} \\ =\text{ 2 + 0.4} \\ =\text{ 2.4} \end{gathered}[/tex]Answer = 2.4
2) 0.5 = 5/10
In its simplest form, we need to divide with a number that is common to both the numerator and the denominator. The number is 5
0.5 as a fraction in its simplest form = 1/2
Find the percent increase for the given original and new quantities in parts a through c.a. Original quantity: 100 New quantity: 106b. Original quantity: 10 New quantity: 16c. Original quantity: 50 New quantity: 56
We can find the percent of increase by means of this formula:
Increase in percent = 100 * (new quantity - original quantity) /original quantity
By replacing the given values into the above formula, we get:
a.
Increase in percent = 100 * (106 - 100) / 100 = 100 * 6 / 100 = 600/100 = 6
Then, the percent of increase equals 6%
b.
Increase in percent = 100 * (16 - 10) / 100 = 100 * 6 / 10 = 600/10 = 60
Then, the percent of increase equals 60%
c.
Increase in percent = 100 * (56- 50) / 50 = 100 * 6 / 50 = 600/50 = 12
Then, the percent of increase equals 12%
Baby McKenna wants to arrange 10 blocks in a row. How many different arrangements can she make?
3,628,800
1) Note that in these arrangements, according to the text the order of the blocks does not matter.
2) When this kind of thing happens we call this is a Permutation, in which the blocks may present in any order, that is not relevant
3) We can calculate it like this:
[tex]P_{10}=10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1=3,628,800[/tex]Thus, there are 3,628,800 different ways to arrange those 10 blocks
I have a practice question that I need answered and explained
Answer:
32(x-1)²/33 +12(y-1/2)²/11 = 1
Explanation:
The equation of the ellipse is:
8x² + 9y² - 16x - 9y + 2 = 0
First, let's rewrite the expression as:
(8x² - 16x) + (9y² - 9y) + 2 = 0
(8x² - 16x) + (9y² - 9y) + 2 - 2 = 0 - 2
(8x² - 16x) + (9y² - 9y) = -2
Now, we need to complete the squares, so we will add 8 and 9/4 to both sides to get:
(8x² - 16x + 8) + (9y² - 9y + 9/4) = -2 + 8 + 9/4
8(x² - 2x + 1) + 9(y² - y + 1/4) = 33/4
8(x - 1)² + 9(y - 1/2)² = 33/4
Finally, multiply by 4 and divide by 33 to get:
4(8)(x-1)² + 4(9)(y - 1/2)² = 4(33/4)
32(x-1)² +36(y-1/2)² = 33
32(x-1)²/33 +36(y-1/2)²/33 = 33/33
32(x-1)²/33 +12(y-1/2)²/11 = 1
Therefore, the answer is:
32(x-1)²/33 +12(y-1/2)²/11 = 1
Jotham needs 12 liters of a 20% alcohol solution. He has a 10% and a 50% solution available. How many liters of the 10% and how many liters of the 50% solutions should he mix to make the 20% solution?
Given:
There are given that the Jotham needs 12 litters of 20% alcohol solution.
Explanation:
Let x be the volume of the 50% solution needed
Then,
The volume of the 10% solution to mix is:
[tex](12-x)[/tex]Then,
The equation to find x is:
[tex]0.50x+0.10\times(12-x)=0.20\times12[/tex]That means,
It say that the volume of the pure alcohol in ingredients is equal to the volume of pure alcohol.
Then,
From the above equation, calculate the value of x
So,
[tex]\begin{gathered} 0.50x+0.10\times(12-x)=0.20\times12 \\ 0.50x+0.10\cdot12-0.10x=0.20\cdot12 \\ 0.40x+0.10\cdot12=0.20\cdot12 \\ 0.40x=0.20\cdot12-0.10\cdot12 \\ x=\frac{12(0.1)}{0.40} \\ x=3 \end{gathered}[/tex]Final answer:
For the 50%, there are 3 litters solution and for the 10%,
[tex]\begin{gathered} 12-x=12-3 \\ =9 \end{gathered}[/tex]Hence, 3 liters of the 50% solution and 9 liters of the 10% solution.
The table below represents the status of different animals.Mammal Bird Reptile Amphibian TotalEndangered 59 75 14TotalThreatened 12 15 32 9371 90 461215168219What is the approximate probability that a selected animal will be a reptile and endangered?
Solution
Animals that are reptiles and endangered = 14
Total animals = 219
[tex]\begin{gathered} Probability\text{ of a selected animal will be reptile and endagered } \\ =\frac{14}{219} \\ =0.0639 \\ =0.06\text{ \lparen 2 decimal places\rparen} \end{gathered}[/tex]HELP PLEASE In the table above, what is the constant of proportionality for width tolength?
Find the output global maximum and global minimum values of the function f(x) = x^3- 9x^2 - 32x + 10(A) Interval = -5, 0Global maximum = (B) Interval = 0,9 Global minimum = (C) Interval =-5, 9.Global maximum =Global minimum =
Given the function f:
We want to find its output global maximum and global minimum values.
To do this, we need to find the deritative of the function first:
Now, we're going to set it equal to zero:
Finally, replace the values x=-5, x=0, and the solutions of the previous equation in the original function. The highest value will be the maximum and the lowest value will be the minimum:
The output global maximum at the interval -5,0 is 34.43.
Anna is using a 6 1/2 pound bag of salt to Pour on snow. After using the salt 2/5 of the bag remains. How many pounds of salt did Anna use to pour on snow
If after using the salt, 2/5 of the salt remains, it means that Anna used 3/5 of the salt in the bag.
A bag contains 6 1/2 pounds of salt, convert this to a fractional number:
[tex]6\frac{1}{2}=6+\frac{1}{2}=\frac{13}{2}[/tex]To find how many pounds of salt she used, multiply 3/5 by the total amount of salt in the bag, this is:
[tex]\frac{3}{5}\cdot\frac{13}{2}=\frac{39}{10}[/tex]She used 39/10 pounds of salt.
Translate the following statement into probability notation news X as the random variable
Let be x the random variable
a)
If we need the probability of x when it is not more than a, we can write it using inequalities as below
[tex]x\le a[/tex]Notice that x can be equal to a but no more than a
And the probability is then
[tex]P(x\le a)[/tex]So, the answer to question a) is the 4th option
b) 'x being at least a' can be written using inequalities in this way:
[tex]x\ge a[/tex]Notice that x can be equal to a, but not less than a
Therefore, the probability is given by the expression
[tex]P(x\ge a)[/tex]So, the answer to question b) is the last option
Find the product of (x - 3) (x - 11)
The expression is given as
[tex](x-3)(x-11)[/tex]ExplanationTo determine the product of the expression.
[tex]\begin{gathered} (x-3)(x-11)=x^2-11x-3x+33 \\ x^2-11x-3x+33=x^2-14x+33 \end{gathered}[/tex]AnswerHence the product of the expression is
[tex]x^2-14x+33[/tex]Using the graph of the function g(x) = log2 (x – 2), what are the x-intercept and asymptote of g(x)?A. The x-intercept is –3, and the asymptote is located at x = 4.B. The x-intercept is –2, and the asymptote is located at y = 3.C. The x-intercept 3, and the asymptote is located at x = 2.D. The x-intercept is 4, and the asymptote is located at y = 2.
Solution
step 1
Step 2
X Intercepts = 3
or (3, 0)
Step 3
Vertical asymptote = 2
Final answer
C. The x-intercept 3, and the asymptote is located at x = 2.