6(h-3).
1) Let's find the GCD between 6, and 18
6h-18 As the GCD is 6 we can write
6(h -3) If we distribute we got the initial expression back.
2) Then the answer is 6(h-3).
Multiplying rational expressions (16x/4).(20/3x^5)
Given:
[tex]\frac{16x}{4}\cdot\frac{20}{3x^5}[/tex]Required:
To multiply the given rational expression.
Explanation:
Consider the given expression,
[tex]\frac{16x}{4}\cdot\frac{20}{3x^5}[/tex]Now
[tex]\begin{gathered} =\frac{4x}{1}\cdot\frac{20}{3x^5} \\ \\ =4\cdot\frac{20}{3x^4} \\ \\ =\frac{80}{3x^4} \end{gathered}[/tex]Final Answer:
[tex]\frac{16x}{4}\frac{20}{3x^{5}}=\frac{80}{3x^4}[/tex]if it rains tomorrow the probability is 0.6 that john will practice his trombone. if it does not rain tomorrow there is only a 0.4 chance that john will practice. suppose the chance of rain tomorrow is 50%what isbthe probability that john will practice his trombone
Let r = rain and p = practice.
Therefore,
[tex]\begin{gathered} Pr\mleft(p\mright)=Pr\mleft(r\mright)\times Pr\mleft(p|r\mright)+1-Pr\mleft(r\mright)\times Pr\mleft(p|notr\mright) \\ Pr(p)=0.5\times0.6\text{ +0.5 x 0.4} \\ =0.3\text{ +0.2} \\ =0.5 \end{gathered}[/tex]Solve the following compound inequality.- X +0 > 5 and 4 + 2x < -12
To solve;
let first take the first one and solve;
-x + 0 >5
-x >5
Divide throughy by -1
whenever you are dividing through by a minus sign, the inequality will change
x <-5
We will now proceed and solve the second inequality;
4 + 2x <-12
subtract 4 from both-side of the ine
Write the number in standard form. (3x104) + (7× 10² The standard form of (3 x 104) + (7 x 102) is
Explanation:
(3x10^4) + (7× 10²)
Simplify:
[tex]=3\times7\times10^4\times10^2[/tex][tex]\begin{gathered} =\text{ 21 }\times10^{4+2} \\ =\text{ 21 }\times10^6 \\ =\text{ 2.1 }\times10^1\times10^6\text{ = 2.1 }\times10^{6+1} \\ =2.1\times10^7 \end{gathered}[/tex]Find the effective rate of interest for 12% compounded quarterlyThe effective rate of interest is %.(Round to three decimal places as needed.)
ANSWER :
12.551%
EXPLANATION :
The effective rate of interest formula is :
[tex]R=(1+\frac{r}{n})^n-1[/tex]where r = nominal rate interest
n = number of compounding in a year
From the problem, the nominal rate interest is 12% or 0.12
n = 4 (compounding quarterly, 4 times in a year)
Using the formula above :
[tex]\begin{gathered} R=(1+\frac{0.12}{4})^4-1 \\ R=0.12551\quad or\quad12.551\% \end{gathered}[/tex]not so good with these ones, thanks for the help!
The inequality expression that represents the number line is |x + 1| > 6
How to determine the inequality expression?The number line represents the given parameter
From the number line, we have the following endpoints
Endpoint 1 = -7
Endpoint 2 = 5
Take the average of the endpoints
This is calculated using
Average = 1/2 * (Endpoint 1 + Endpoint 2)
So, we have
Average = 1/2 * (-7 + 5)
Evaluate
Average = -1
Calculate half the difference of the endpoints
This is calculated using
Half difference = 1/2 * (Endpoint 2 - Endpoint 1)
So, we have
Half difference = 1/2 * (5 + 7)
Evaluate
Half difference = 6
The inequality expression is then represented as
|x - Average| > Half difference
This gives
|x + 1| > 6
Hence, the inequality expression is |x + 1| > 6
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Theodore needs to mix a 20% saline solution with a 60% saline solution to create 200 milliliters of a 34% solution. how many millimeters of each solution must Theodore use?
130 ml of solution 1 and 70 ml of solution 2
Explanation
Step 1
Let
Volume of solution 1 ( 20% saline solution)=x
Volume of solution 2( 60 % saline solution)=y
Step 2
replace
Theodore needs to mix a 20% saline solution with a 60% saline solution to create 200 milliliters of a 34% solution
the volume of salt ( in solution 1)= 0.2 *volume of the solution 1
the volume of salt ( in solution 2)= 0.6 *volume of the solution 1
the volume of salt ( in mix)= 0.34 *volume of mix
replace,
[tex]\begin{gathered} 0.2x+0.6y=0.34*200\text{ } \\ 0.2x+0.6y=68\text{ Equation(1)} \end{gathered}[/tex]Also
volume os solution 1 + volume of solution 2 = volume of mix
replace,
[tex]x+y=200\text{ Equation (2)}[/tex]Step 3
use equatino (1) and (2) to find x and y
a) isolate x form equation (2)
[tex]\begin{gathered} x+y=200 \\ x=200-y\text{ Equation (3)} \end{gathered}[/tex]b) replace equation (3) in equation (1)
[tex]\begin{gathered} 0.2(200-y)+0.6y=68 \\ 4-0.2y+0.6y=68 \\ 0.4y=68-40 \\ 0.4y=28 \\ y=\frac{28}{0.} \\ y=70 \end{gathered}[/tex]c) replace the valur of y =70in equation (3) to find x
[tex]\begin{gathered} x=200-y \\ x=200-70 \\ x=130 \end{gathered}[/tex]If 14g of a radioactive substance are present initially and 9yr later only 7g remain, how much of the substance will be present after 13 yr?
To begin with, let us first write out the formula for the exponential form
[tex]y=b^{rt}[/tex]Given the initial parametrs
[tex]y=14b^t^{}[/tex]Thus
[tex]145^9=7[/tex][tex]b^{-9}=\frac{1}{2}[/tex]Using exponential laws
[tex]b=\frac{1}{(\frac{1}{2})^{\frac{1}{-\frac{1}{9}}}}[/tex]W will soon see that
[tex]b=2^{\frac{1}{9}}[/tex]Hence after 13 years, the substance left will be;
[tex]\begin{gathered} 14(2^{\frac{1}{9}})^{-13}=5.144070729 \\ \approx5.144g \end{gathered}[/tex]What type of transformation is shown?Select from the drop-down menu to correctly identify the transformation.
Answer:
[tex]\text{ Reflection}[/tex]
Explanation:
Here, we want to get the type of transformation showed
The original shape is what we have on the left, the shape after transformation is what we have on the right
What we can notice is that despite the fact that the y-values of the coordinates remain the same, the x-coordinates values changed from negative to positive
For example: B changed from (-2,1) to (2,1)
The rule is:
[tex](x,y)\text{ to (-x,y)}[/tex]This is characteristic of reflection over the y-axis
Thus, the correct transformation here is reflection
what's 1,776 x 32 and please show work
we have to solve:
[tex]1776\times32[/tex]So solving it :
[tex]\begin{gathered} 1776\times30+1776\times2 \\ 53280+3552 \\ 56832 \end{gathered}[/tex]2. A Regular Octagon rotates counterclockwise about its center. At how many differentangles will the Octagon map onto itself?A regular Octagon has equal sides. Any rotations by multiples of degreesabout the center maps it onto itself.3. If a trapezoid is non-isosceles, then it has lines of reflection?4. A rectangle has 2 lines of symmetry which are also called
A regular Octagon is a Polygon with 8 equal sides.
Since the Octagon is a regular Octagon then all the sides are equal and all the interior angles are the same.
In one complete rotation (0-360 degree), the angles in which the regular octagon will map into itself can be derived by;
[tex]d=\frac{360}{8}=45^0[/tex]So, on an interval of 45 degree the Octagon maps onto itself.
Any rotation of 45 degree will map it onto itself.
The angle in which the regular octagon will map into itself are;
[tex]45^0,90^0,135^0,180^0,225^0,270^0,315^0,360^0[/tex]There are 8 different angles in which the Regular Octagon will map onto itself.
listed above are the 8 angles.
about 34 out of every 320 people are left handed. if 3360 student attend high school, about how many are left handed?
Let's begin by listing out the information given to us:
34 out of 320 are left-handed
n = 3360 students
To find the number of left-handed students, we calculate thus:
I it takes 40 seconds to walk 75 steps. how many minutes does it take to get 5000 steps in?then 7500?
It takes 45 minutes to get 5000 steps
Explanation:Given that:
40 seconds = 75 steps
Let
x seconds = 5000 steps
Then
75x = 40 * 5000
75x = 200000
x = 200000/75 seconds
To convert this to minutes, we divide the result by 60
x = 200000/(75 * 60) minutes
= 200000/4500 = 44.44 minutes
This is approximately 45 minutes of walking
I dont know where to begin to solve this with my kiddo
Since those are consecutive interior angles, we can conclude:
[tex]\begin{gathered} 4x+6x=180 \\ _{\text{ }}add_{\text{ }}like_{\text{ }}terms\colon \\ 10x=180 \\ _{\text{ }}solve_{\text{ }}for_{\text{ }}x\colon \\ \frac{10x}{10}=\frac{180}{10} \\ x=18 \end{gathered}[/tex]Answer:
18
EInitial Knowledge CheckQuestion 4AdoleFor the third week of July, Kim Gonzales worked 50.75 hours. Kim carns $10.40 an hour Her employer pis overtime for all hours worked in een ofper week and pays 1.5 times the hourly rate for overtime hours.Calculate the following for the third week of July (round your responses to the nearest cen if necessity)X?1. Regular pay amount2. Overtime pay3. Gross Day$0$0I Don't KnowSubmly2022Mew All Rifles Termine Pry49"Type here to searchORA
Step 1:
Pay per hour for a regular work = $10.40
Pay per hour for an overtime work = 1.5 x $10.4 = $15.6
Regular hour = 40
Step 2
[tex]\begin{gathered} \text{Regular pay = 40 }\times\text{ 10.40 = \$416} \\ Overtime\text{ pay = 10.75 }\times\text{ 15.6 = \$167.7} \\ Gross\text{ pay = \$416 + \$167.7 = \$583.7} \end{gathered}[/tex]. A consumer advocacy group claims that the mean mileage for the Carter MotorCompany's new sedan is less than 32 miles per gallon. That isHo: Carter Motor Company's new sedan is less than 32 miles per gallonWrite the type I error for the test
Solution:
In this case, null hypothesis is that mean is not less than 32.
Hence, type I error is to conclude that the true mean is less than 32 miles per gallon, even though it is not.
This could lead to a lawsuit where the Carter Motor Company might have to pay a fine even though they are innocent.
Remember that,
Type I error = rejecting null hypothesis even if it is true.
Type 1 error can only occur when you reject
[tex]H_0[/tex]Hence,
The type 1 error for the test is
Reject the claim that the mean is equal to 32 miles per gallon when it is actually less than 32 miles per gallon
Amanda has $616.78 in her checking account. She makes deposits of $42.66 and $83.44. She writes checks for $33.69, $54.57, and $9.35 estimate the new balance in her checking account
Given:
Given the word problem, we can deduce the following information.
1. Amanda has $616.78 in her checking account.
2. She deposited 42.66 and $83.44.
3. She writes checks for $33.69, $54.57, and $9.35.
To find the new balance in her checking account, we use the formula:
New balance= Previous Balance+ Deposits-Withdrawals
Based on the given information, we let:
Previous Balance = $616.78
Deposits = $42.66 + $83.44 = $126.1
Withdrawals = $33.69 + $54.57 + $9.35 =$97.61
We plug in what we know in the formula:
New balance= Previous Balance+ Deposits-Withdrawals
= $616.78 +$126.1-$97.61
Calculate
New balance= $645.27
Therefore, the answer is $645.27.
4x+5y=7 Y=3x+9What is x? What is y?
As given by the question
There are given that the system of the equation:
[tex]\begin{gathered} 4x+5y=7\ldots(1) \\ y=3x+9\ldots(2) \end{gathered}[/tex]Now,
Put the value of equation (2) into equation (1) instead of y:
So,
From the equation (1):
[tex]\begin{gathered} 4x+5y=7 \\ 4x+5(3x+9)=7 \\ 4x+15x+45=7 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 4x+15x+45=7 \\ 19x+45=7 \\ 19x=7-45 \\ 19x=-38 \\ x=-\frac{38}{19} \\ x=-2 \end{gathered}[/tex]Then,
Put the value of x into equation (2) to find the y:
So,
[tex]\begin{gathered} y=3x+9 \\ y=3(-2)+9 \\ y=-6+9 \\ y=3 \end{gathered}[/tex]Hence, the value of x and y is shown below:
[tex]\begin{gathered} x=-2 \\ y=3 \end{gathered}[/tex]the area A of the rectangle shown is described with the inequality 100[tex] \leqslant [/tex]A[tex] \leqslant [/tex]1,000. Write and solve a compound inequality for x.
if the circle area is 8 in and the pi is 3.14 round to the nearest hundredth
When the circle area is 8 in and the pi is 3.14, the radius is 1.6 inches.
What will the radius be?The area of a circle is calculated thus:
Area = πr²
In this case, the area is 8 and π = 3.14. We will slot them into the formula. This will be:
Area = πr²
8 = (3.14 × r²)
Divide
r² = 8 / 3.14
r² = 2.55
r = ✓2.55
r = 1.6
The radius is 1.6 inches.
Note that the question is incomplete but was solved based on the likelihood that the radius will be found.
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Solve X^2 = -54 where x is a real number
We are given the following equation:
[tex]x^2=-54[/tex]To solve this equation we will take the square root to both sides:
[tex]x=\sqrt[]{-54}[/tex]We are given that "x" is a real number, but the square root of a negative number does not exist in the real numbers therefore, this equation has no solution.
what is 82827273636277218288281828272717×0
Any product that involves a number times zero will always give zero for answer.
Therefore just type "0" in the answer for the problem.
Given the point (-7,-4) and the slope m=5, write and equation in SLOPE INTERCEPT FORM!
Given the point (-7,-4) and the slope m=5, write and equation in SLOPE INTERCEPT FORM!
we know that
the equation in slope intercept form is equal to
y=mx+b
we have
m=5
point (-7,-4)
substitute the given values in the expression above
-4=5*(-7)+b
solve for b
-4=-35+b
b=35-4
b=31
therefore
y=5x+31Find the length of the segment with endpoints at (-2,1) and (-5,4). Roundyour answer to the nearest tenth. (1 decimal place)
The formula to find the distance between two points A and B is
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1_{})^2+(y_2-y_1)^2} \\ \text{ Where} \\ A(x_1,y_1) \\ B(x_2,y_2) \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} A(x_1,y_1)=(-2,1) \\ B(x_2,y_2)=(-5,4) \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-5-(-2))^2+(4-1)^2} \\ d=\sqrt[]{(-5+2)^2+(4-1)^2} \\ d=\sqrt[]{(-3)^2+(3)^2} \\ d=\sqrt[]{9+9} \\ d=\sqrt[]{18} \\ d=4.2 \end{gathered}[/tex]Therefore, the length of the segment with endpoints at (-2,1) and (-5,4) is 4.2 units.
Find A. Measure of angle AB. Measure arc CEC. Measure of angle CD. Measure of angle DE. Measure of angle ABE
A chord is a segment that links two points from a circumference. When two chords share an extreme they form an angle in that point and an arc with their remaining extremes. The angle is known as an inscribed angle and the arc is its intercepted arc. For any inscribed angle in a circle its measure is the half of the measure of its intercepted arc. As you can see angle A is formed by the chords AB and AD which means that arc BD is its intercepted arc. Then the measure of A is given by:
[tex]\begin{gathered} \angle A=\frac{1}{2}\measuredangle BD=\frac{1}{2}78^{\circ} \\ \angle A=39^{\circ} \end{gathered}[/tex]Then we have to find the measure of arc CE. It's the intercepted arc of angle EBC which has a measure of 20°. Then the measure of arc CE is the double of this quantity:
[tex]\measuredangle CE=2\angle EBC=2\cdot20^{\circ}=40^{\circ}[/tex]Angle C is the inscribed angle of the arc BD just like angle A which means that the measure of C is the same that the measure of A. Then we get:
[tex]\angle C=\angle A=39^{\circ}[/tex]The angle D has arc AC as its intercepted arc so its measure is given by:
[tex]\angle D=\frac{1}{2}\measuredangle AC=\frac{1}{2}84^{\circ}=42^{\circ}[/tex]Arc AC is also the inscribed arc of angle ABC which means that the measure of this angle is the same as the measure of D:
[tex]\angle ABC=\angle D=42^{\circ}[/tex]Angle ABE is given by the sum of angle ABC and angle B so its measure is:
[tex]\angle ABE=\angle ABC+\angle B=42^{\circ}+20^{\circ}=62^{\circ}[/tex]AnswersA. 39°
B. 40°
C. 39°
D. 42°
E. 62°
Which sports location had the largest increase in the attendance in month 1 to the attendance in month 7?
For this problem, we are given the attendance graph of three sports centers in the span of 7 months. We need to identify which of the three centers had the largest increase in attendance during this time.
To solve the problem, we need to compare the attendance of each sports center in month 7 with their attendance in month 1.
The Coors field seems to have a growth in attendance of 2.5 horizontal bars, the Petco Park seems to have a growth in attendance of 4.8 bars and the Turner field seems to have a growth in attendance of 3.9 bars. With thi,s we conclude that Petco Park saw the highest growth in attendance.
The answer is Petco Park.
Every Sunday morning, Opal, Lisa, Talia, and Cora meet for breakfast at the Bagel Shop 1 They share the bill equally and each pay $2 toward the tip. The expression - 1 - 2 represents 1 the amount each friend pays, where x is the amount of the bill before the tip. 1 What do the parts of the expression = x + 2 represent? 4 1 1) The term a represents the amount each friend pays toward the ? 4 4 The term 2 represents the amount each friend pays toward the ? tip bill
Since the expression:
[tex]\frac{1}{4}x+2[/tex]represents the amount each friend pays, and x is the amount of the bill before the tip, and the tip is divided in 4 for each friend to pay the same amount, then the expression:
[tex]\frac{1}{4}x[/tex]Is a quarter of the total amount of the bill, and represents the amount each friend pays toward the bill.
Since each friend pays $2 in addition, the term 2 represents the amount each friend pays toward the tip.
Since Talia will pay twice the amount that each friend is supposed to pay, then the expression which represents the total amount that Talia will pay, is:
[tex]2(\frac{1}{4}x+2)[/tex]What is the balance at compound interest if the principal is $345 the annual rate is 5.5% and the time is 42 months.
At compound interest, the amount in the account
how do i put this i dont really know how to explain it
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph:
f(x) and g(x)
Step 02:
functions:
we must analyze the graph to find the solution.
graph:
f(x) = g(x)
positive x-coordinate = 2
The answer is:
positive x-coordinate = 2
what is the solution of x- 16>8
x - 16 > 8 Inequality
Isolate x
x > 8 + 16
Then solution is
x > 24
(all numbers bigger than 24)
