In the given rectangle :
Length = (5x - 2) ft
Width = 2 ft
Area of rectangle is express as the product of length and width
Area of rectangle = Length x Width
Area of rectangle = (5x - 2) x 2
Simplify : (5x - 2) x 2 = 10x - 4
Area of rectangle = 10x - 4
Answer : Area of rectangle = 10x - 4
The domain of g(f(x)) is:
the square root must be positive, so:
[tex]\begin{gathered} 3x-1\ge0 \\ 3x\ge1 \\ x\ge\frac{1}{3} \end{gathered}[/tex]the domain of g(f(x)) is:
[tex]D\colon x\ge\frac{1}{3}[/tex]5. . Find the surface area of each object to the a nearest tenth of a square unit. d=0.003 m b) су fa a) d=2.5 cm 16 cm re wooden rod 16 m flag pole
The flag pole is a cylinder, the surface area of the cylinder is given by:
[tex]SA=2\pi r^2+2\pi rh[/tex]Where:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{0.003}{2}=0.0015m \\ h=16m \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} SA=2\pi\cdot(0.0015)^2+2\pi(0.0015)(16) \\ SA\approx0.2m^2 \end{gathered}[/tex]Answer:
0.2 m²
Find the mean for this list of numbers8 40 50 85 1 5 46 65 41 13 34 67 53 71 44
Answer
Explanation
Given:
8, 40, 50, 85, 1, 5, 46, 65, 41, 13, 34, 67, 53, 71, 44
To determine the mean for the given list of numbers, we note first that the mean is the same as the average value in a data set. We add up all the data values to get the sum and divide the sum by the count of the number of values.
We can use the formula:
Mean = Sum of the terms/Number of terms
where:
Sum of the terms = 8+40+50+85+1+5+46+65+41+13+34+67+53+71+44=623
Number of terms = 15
So,
[tex]\begin{gathered} Mean=\frac{623}{15} \\ Calculate \\ Mean=41.533 \end{gathered}[/tex]Therefore, the mean is 41.533.
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win$13. If you roll a 4 or 5, you win $4. Otherwise, you pay $6.a. Complete the Table: List the X values, where X is the profit, from smallest to largest. Round to4 decimal places where appropriate.Probability Distribution TableХP(X)b. Find the expected profit. $(Round to the nearest cent)
We have a six-sided die
possible outcome
[tex]1,\text{ 2,3,4,5,6}[/tex]if you roll a 6 you get $13
if you roll a 4 or 5 you get $4
if otherwise, you get 1,2,3 you will them $6
[tex]\begin{gathered} \text{Probability of getting \$13=}\frac{1}{6} \\ \\ \text{Probability of getting \$4=}\frac{2}{6}=\frac{1}{3} \\ \\ \text{Probability of paying them \$6=}\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]We are asked to complete the table from smallest to biggest
Part B
The expected profit.
[tex]\begin{gathered} -6(\frac{1}{2})+4(\frac{1}{3})+13(\frac{1}{6}) \\ \\ =-3+\frac{4}{3}+\frac{13}{6} \\ =\text{ \$0.50} \end{gathered}[/tex]Part C
If you play many games you will likely win on average very close to $0.50 per game because the expected profit is $0.50
Part D
Yes, since the expected value is positive you will likely to come home with more money if you played more games
what does x equal if -3/6 x = -2
-3/6 is multiplying on the left, then it will divide on the right. Remember that divide by a fraction is the same as multiply by it inverse. The inverse of -3/6 is -6/3.
[tex]\begin{gathered} x=-2\cdot(\frac{-6}{3}) \\ x=-2\cdot(-2) \\ x=4 \end{gathered}[/tex]The answer for this problem Find the equation of line j.The blue line is line j
ANSWER
[tex]y=-\frac{1}{5}x[/tex]EXPLANATION
As we can see, line j passes through the origin, so its y-intercept is zero and the equation has the form,
[tex]y=mx[/tex]To find the slope we have to use the formula,
[tex]m=\frac{\Delta y}{\Delta x}[/tex]In this graph,
Δy = 1 and Δx = 5, but the line is inclined to the left, so the slope is negative,
[tex]m=-\frac{1}{5}[/tex]And the equation is,
[tex]y=-\frac{1}{5}x[/tex]Carrie pays a monthly fee of $8 to stream movies online. She also pays a fee every time she rents a movie. Last monthCarrie rented 6 movies, and her total bill for the month was $32.Select from the drop-down menu to correctly complete each statementThe monthly fee for Carrie to stream movies is Choose... Carrie also pays Choose... every time she rents amovie.12345Next
Let R be the amount (in dollars) that Carrie pays every time she rents a movie. Now, if the last month Carrie rented 6 movies, her total bill for the month was $32, and since she pays a monthly fee of $8 we can set the following equation:
[tex]8+6R=32.[/tex]Subtracting 8 from the above equation we get:
[tex]\begin{gathered} 8+6R-8=32-8, \\ 6R=24. \end{gathered}[/tex]Dividing the above equation by 6 we get:
[tex]\begin{gathered} \frac{6R}{6}=\frac{24}{6}, \\ R=4. \end{gathered}[/tex]Therefore Carry pays $4 every time she rents a movie.
Answer:
The monthly fee for Carrie to stream movies is $8. Carry also pays $4 every time she rents a movie.
Find each of the following quotients express your final answers in simplest form you do not need to convert them to mixed numbers
Given
[tex]\frac{6}{7}\div\frac{5}{14}[/tex]Solution
The division sign will change to multiplication and then the denominator and numerator would interchange
[tex]\frac{6}{7}\times\frac{14}{5}=\frac{6}{1}\times\frac{2}{5}=\frac{12}{5}[/tex]The final answer
[tex]\frac{12}{5}[/tex]Two six-part spinners are numbered 1 to 6. What is the probability that both numbers will match if the spinners are spun once each?
There are 36 possible outcomes
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
There are 6 matching outcomes
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
P(matching) = number of matching / total
= 6/36
= 1/6
When k³-17k+32 is divided by k+5,find the quotient and match the letters to the terms to fill in L N O P Q ? Can you show me how to set it up and the answer please
---------------------------
k + 5 l k^3 - 17 k + 32
First we can see terms k+5 is the letter D and k^3 is letter E , -17 k letter F and
32 is letter G
Then we search for a term that multiplied by k equals k^3, which is k^2 , this is going to be our letter A
We multiply ( k + 5 ) by k^2 , the result is k^3 + 5 k^2 , we place these terms below k ^3 and -17 k changing the signs,
k ^3 - 17 k
- k^3 - 5 k ^2
k^3 is cancelled and since 17 k and -5 k^2 are not similar we don't operate them, they continue for our next round of division. Until now we can see -k^3 is letter H and -5k^2 is letter l.
Afterwards, we search for a term that multiplied by k equals -5 k^2, which is -5k, this is going to be the letter B. Then we multiply -5 k by ( k + 5), the result is -5k^2 and -25 k. Then we change the signs before placing them below our previous result. Letter j is -5 k^2 and letter k is -17 k
- 5 k^2 - 17 k + 32
+ 5 k^2 + 25 k
5 k^2 is cancelled and the result of adding -17 k to 25k is 8 k. It implies letter L is 5 k^2 and letter M is 25 k
Then we search for a term that multiplied by k equals 8 k, which is 8. It implies letter C is 8. We multiply 8 by ( k + 5), the result is 8k + 40. Then we change the signs before placing them below our previous result. Letter N is 8k
8 k + 32
-8 k - 40
8 k is cancelled and the result of subtracting 40 to 32 is -8. Doing so we find letter Q is -8. Letter O is -8 k and letter P is -40
When Akiko finished the next level of her video game, she lost 20points for each of the five targets she missed and was penalized 135points for taking too long. Write the total change to her score as aninteger.
Total change to Akiko's score = 235 points
Explanations:The number of targets missed by Akiko = 5
Number of points lost for each of the targets = 20
Total number of points lost for the 5 targets = 20 x 5
Total number of points lost for the 5 targets = 100 points
The total number of points used for penalization = 135 points.
Total change to Akiko's score = 100 + 135
Total change to Akiko's score = 235 points
Using the number line represents -4 + 5. What’s the sum?
The Number Line
The number -4 is 4 units to the left of the origin as shown below:
To add +5 to the number -4, we draw an arrow of length 5 pointing to the right. The number pointed at the tip of the arrow is the result of the sum.
The sum is 1
Answer:1
Step-by-step explanation:
the coordinates of DEFG are D(2,-1), E(5,-2) F(4,-5), and G(1,-4). Describe in coordinate mapping notation a translation that will move vertex E to the origin.
A translation is given as:
[tex](x,y)\rightarrow(x+a,y+b)[/tex]We need to find the translation that takes E to the origin that is:
[tex](5,-2)\rightarrow(5+a,-2+b)=(0,0)[/tex]Then we have the equations:
[tex]\begin{gathered} 5+a=0 \\ a=-5 \end{gathered}[/tex]and
[tex]\begin{gathered} -2+b=0 \\ b=2 \end{gathered}[/tex]Therefore the translation is:
[tex](x,y)\rightarrow(x-5,y+2)[/tex]Complete the average rate of change (ARC) for the function H(n) = 5/ n + 1 On the interval [2, 10] ARC[2, 10] = ________
Averate rate of change:
[tex]\begin{gathered} \lbrack a,b\rbrack \\ \\ ARC=\frac{H(b)-H(a)}{b-a} \end{gathered}[/tex]For the given interval:
[tex]\begin{gathered} \text{ARC}_{\lbrack2,10\rbrack}=\frac{H(10)-H(2)}{10-2} \\ \\ \text{ARC}_{\lbrack2,10\rbrack}=\frac{\frac{5}{10+1}-\frac{5}{2+1}}{8} \\ \\ \text{ARC}_{\lbrack2,10\rbrack}=\frac{\frac{5}{11}-\frac{5}{3}}{8} \\ \\ \text{ARC}_{\lbrack2,10\rbrack}=\frac{\frac{15-55}{33}}{8} \\ \\ \text{ARC}_{\lbrack2,10\rbrack}=\frac{-\frac{40}{33}}{8} \\ \\ \text{ARC}_{\lbrack2,10\rbrack}=\frac{-40}{33\cdot8} \\ \\ \text{ARC}_{\lbrack2,10\rbrack}=-\frac{40}{264} \\ \\ \text{ARC}_{\lbrack2,10\rbrack}=-\frac{5}{33}=-0.\bar{15} \end{gathered}[/tex]Then, the averate rate of change of the given function in the interval {2,10} is -5/33 (or -0.15)a) f(n) = f(n-1).4; f(1) = 4b) f (n) = 4n +1c) f(n) = f(n-1) +4; f(1) = 4d) f(n) = 1.4"
In Step 1, we have 4 dots. Therefore: f(1)=4
In Step 2, we have 16 dots. Therefore: f(2)=16
In Step 3, we had 64 dots. Therefore: f(3)=64
We observe that each of the f(n) is 4 raised to the particular n.
[tex]\begin{gathered} f(1)=4^1=4 \\ f(2)=4^2=16 \\ f(3)=4^3=64 \end{gathered}[/tex]Therefore, the next term is obtained through the multiplication of the previous term by 4.
Therefore, the recursive formula which fits the dot will be:
[tex]f(n)=f(n-1)\cdot4,\text{ f(1)=4}[/tex]What is the initial temperature of the liquid and when is the temperature at 100°F?T(m)=101e^-0.03m+67
a) The initial temperature of the liquid is simply the temperature of the liquid at time m = 0
Thus, we have the temperature to be:
[tex]\begin{gathered} T(m)=101e^{-0.03m}+67 \\ \Rightarrow T(0)=101e^{-0.03\times0}+67 \\ \Rightarrow T(0)=101e^0+67 \\ \Rightarrow T(0)=101(1)^{}+67 \\ \Rightarrow T(0)=101^{}+67 \\ \Rightarrow T(0)=168^oF \end{gathered}[/tex]The initial temperature of the liquid is 168 degrees Fahrenheit
b) The time when the temperature of the liquid will reach 100 degrees Fahrenheit is obtained as follows:
[tex]\begin{gathered} T(m)=101e^{-0.03m}+67 \\ \Rightarrow100=101e^{-0.03m}+67 \\ \Rightarrow100-67=101e^{-0.03m} \\ \Rightarrow33=101e^{-0.03m} \\ \Rightarrow\frac{33}{101}=e^{-0.03m} \\ \Rightarrow e^{\mleft\{-0.03m\mright\}}=\frac{33}{101} \end{gathered}[/tex]Now, take the natural logarithm of both sides, as follows:
[tex]\begin{gathered} e^{\mleft\{-0.03m\mright\}}=\frac{33}{101} \\ \Rightarrow\log _ee^{\{-0.03m\}}=\log _e(\frac{33}{101}) \\ \Rightarrow(-0.03m)\log _ee=\log _e(\frac{33}{101}) \\ \Rightarrow(-0.03m)(^{}1)=\log _e(\frac{33}{101}) \\ \Rightarrow-0.03m=\log _e(\frac{33}{101}) \\ \Rightarrow m=\frac{1}{-0.03}\times\log _e(\frac{33}{101}) \\ \Rightarrow m=\frac{1}{-0.03}\times-1.1186=\frac{-1.1186}{-0.03}=37.39 \\ \Rightarrow m=37.4\text{ minutes (to the nearest tenth of a minute)} \end{gathered}[/tex]The time when the temperature of the liquid will reach 100 degrees Fahrenheit is 37.4 minutes
Emily took an airplane trip that was 880 miles long . The trip took 8 hours . If the plane flew the same amount of miles each hour , how many miles did the plane travel per hour ?
Given data:
The given distance is d=880 miles.
The given time is t=8 hr.
The expression for the speed is,
s=d/t
Substitute the given values in the above expression.
s=(880 miles)/(8 hours)
=110 miles/h
Thus, the speed is 110 miles/hour.
Using the vertical line test, does the following relation represent a function?
Explanation: For our relation, we have the x-values as inputs and the y-values as outputs. All we need to know is that for a relation to be a function for each input there will be just one and no more than one corresponding output, if so, it is not a function.
Step 1: Let's take a look at our graph to visualise the relation between inputs (x-values) and outputs (y-values)
As we can see above, for x=-4 we have the output 3, for x=6
Solve the equation, separate multiple answers with comma of necessary
On solving the given cubic equation, the result obtained are
p = 0, -2 , -5
What is cubic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A three degree equation is known as cubic equation.
Here
The given cubic equation is
[tex]3p^3+21p^2+30p = 0[/tex]
Now,
[tex]3p^3 +21p^2 + 30p= 0\\3p(p^2 + 7p +10)= 0\\3p(p^2 + 2p+5p+10 = 0)\\3p[p(p+2)+5(p+2)] = 0\\3p(p +2)(p+5) = 0[/tex]
3p = 0 or p + 2 = 0 or p + 5 = 0
p = 0 or p = -2 or p = -5
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a triangle region has sides measuring 25, 35, 15 feet find the measure of the largest angle in the region
Remember that
In any triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle
so
In this problem
The largest angle is opposite the 35 units side
therefore
Applying the law of cosines
[tex]c^2=a^2+b^2-2abcosC[/tex]where
c=35 ft
a=25 ft
b=15 ft
C is the largest angle (angle between side a and side b)
substitute
[tex]35^2=25^2+15^2-2(25)(15)cosC[/tex]Solve for cosC
[tex]cosC=\frac{25^2+15^2-35^2}{2(25)(15)}[/tex][tex]C=120^o[/tex]The measure of the largest angle is 120 degreesfind the length of the third side. if necesary write in simplest radical form.
Recall that in a right triangle we can use the Pythagorean theorem:
[tex]c^2=a^2+b^2,[/tex]where a and b are the lengths of the legs and c is the length of the hypotenuse.
Now, the given triangle has legs of length 5 and 2, therefore:
[tex]c^2=5^2+2^2=25+4=29.[/tex]Solving the above equation for c we get:
[tex]c=\sqrt[]{29}.[/tex]Answer:
[tex]\sqrt[]{29}.[/tex]the slope intercept form of a linear equation is y = mx + b. how do I solve the equation for x?
Here, we want to make x the subject of the formula
We have this as;
[tex]\begin{gathered} y\text{ = mx + b} \\ \\ y-b\text{ = mx} \\ \\ x\text{ = }\frac{y-b}{m} \end{gathered}[/tex]Jullas monthly gasoline bill dropped from 33.57 last month, to 30.83 this month. Find thepercent decrease, Round to the nearest whole percent.
To determine the percent of decrease we use the following formula:
[tex]\frac{Old\text{ value-New value}}{Old\text{ Value}}\times100.[/tex]Substituting:
[tex]\begin{gathered} Old\text{ value=33.57,} \\ New\text{ value=30.83} \end{gathered}[/tex]in the formula, we get:
[tex]\frac{33.57-30.83}{33.57}\times100.[/tex]Simplifying the above result, we get:
[tex]\approx8\%.[/tex]Answer: [tex]\begin{equation*} 8\%. \end{equation*}[/tex]Problem: A scale model of an airplane has a scale of inch = 2 feet the actual length of the plane is 40 feet long. How long is the scale model?
The scale is:
[tex]\frac{1}{4}inch=2\text{ fe}et[/tex]This means that every 1/4 inch in the scale model represents 2 feet of the real plane.
The real length of the plane is:
[tex]40\text{ ft}[/tex]To solve this problem is useful to take the scale:
[tex]\frac{1}{4}inch=2\text{ fe}et[/tex]And find how many inches represent just 1 foot. We can find this by dividing both sides by 2:
[tex]\frac{1}{8}\text{inch}=1\text{feet}[/tex]Now that we know that 1 foot represents 1/8 inches, the last step is to multiply 40 feet by 1/8 and we will find the length of the plane in the scale model:
[tex]40\times\frac{1}{8}\text{inch}=\frac{40}{8}\text{inch}=5\text{inch}[/tex]Answer: the length in the scale model is 5 inches.
help me solve this please
The solution of equation 4(2+3c)=56 is c=4.
What is equation?.Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
4(2+3c) = 56
8+12c=56
12c = 48
c = 48/12
c= 4
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A dairy needs 220 gallons of milk containing 7% butterfat. How many gallons each of milk containing 8% butterfat and milk containing 3% butterfat must be used to obtain the desired 220 gallons?
ExplAnation
Given 220 gallons of milk containing 7% butterfat.The number of gallons each of milk containing 8% butterfat and milk containing 3% butterfat must be used to obtain the desired 220 gallon
Let a = gallons of 8% butterfat milk needed
Let b = gallons of 3% butterfat milk needed
0.08a = gallons of butterfat in 8% milk
0.03b = gallons of butterfat in 3% milk
[tex]a+b=220---1[/tex]Also;
[tex]\begin{gathered} \frac{0.08a+0.03b}{220}=0.07 \\ 0.08a+0.03b=200\times0.07 \\ 0.08a+0.03b=14----2 \end{gathered}[/tex]Isolate for a in equation 1 and substitute in equation 2
[tex]\begin{gathered} \begin{bmatrix}0.08\left(220-b\right)+0.03b=14\end{bmatrix} \\ \begin{bmatrix}17.6-0.05b=14\end{bmatrix} \\ 0.05b=17.6-14 \\ 0.05b=3.6 \\ b=\frac{3.6}{0.05} \\ b=72 \end{gathered}[/tex]Hence;
[tex]\begin{gathered} a+72=220 \\ a=220-72 \\ a=148 \end{gathered}[/tex]Answer: 148 gallons of 8% butterfat milk are needed 72 gallons of 3% butterfat milk are needed
at what rate is a rider descending when she is 57 feet above ground level?
We have a Ferris wheel with radius r = 38 ft.
It takes 5 minutes to complete a revolution, so we can calculate the tangent speed as:
[tex]\begin{gathered} v=\frac{C}{t} \\ v=\frac{2\pi r}{t} \\ v=\frac{2\pi\cdot38ft}{5\min}\cdot(\frac{1\min }{60s}) \\ v\approx0.795870\frac{ft}{s} \end{gathered}[/tex]We calculate the module of this speed as the distance travelled in one revolution (one circumference) divided by the time it takes to make that one revolution.
If we consider that the center of the wheel is 38 ft above the ground (that means that the bottom part of the wheel is at ground level), then 57 ft is a height that is 1.5 times the ratio.
Then, we have to find the angle from the center at which y = 57 ftis located:
We can relate h = 19 with the radius r = 38 and the angle α as:
[tex]\begin{gathered} h=r\cdot\sin \alpha \\ \sin \alpha=\frac{h}{r}=\frac{19}{38}=0.5 \\ \alpha=\arcsin (0.5)=30\degree \end{gathered}[/tex]Then, we know that the angle is 30°.
Then, if we draw the components of the speed, we get:
We are only interested in the vertical component, so we can use the graph to relate Vy to the module of the speed and the angle we have already calculated:
[tex]\begin{gathered} V_y=v\cdot\cos (\alpha) \\ V_y=0.795870\cdot\cos (30\degree) \\ V_y\approx0.795870\cdot0.866025 \\ V_y\approx0.689 \end{gathered}[/tex]Answer: she is descending at a rate of 0.689 ft/s.
where is the function h increasing and deceasing (use interval notation label which is which)
According to the given graph, we have two increasing intervals and one decreasing interval.
Remember, the function increases when y-values increase while x-values increase. On the other hand, the function decreases when y-values decrease while x-values increase.
Having said that, we can define the following intervals.
[tex]\begin{gathered} I\colon(-\infty,-1)\cup(1,\infty) \\ D\colon\mleft\lbrack-1,1\mright\rbrack \end{gathered}[/tex]Where I show where the function increase, and D shows where the function decreases.
A second way to express the intervals is as follows.
The function h increases:
[tex]\mleft\lbrace x|(-\inftyThe function h decreases:[tex]\mleft\lbrace x|-1\leq x\leq1\mright\rbrace[/tex]Seven less than x and x=3
EXPLANATION
If x=3, then seven les than x is equal to 7-3 = 4
perimeter od the garden is now twice the perimeter of the old garden. the expression 12w+16 represents the perimeter of the new garden, where w represent the width of thr old garden . the expression that represents the perimeter is?
perimeter of the garden is now twice the perimeter of the old garden.
Perimeter of new garden = 2(Perimeter of old garden
Expression for the perimeter of new garden is 12w + 16
where, w represent the width of the garden,
So, Perimter of new garden is twice the perimeter of the old garden.
12w + 16 = 2 (Perimeter of old garden)
Perimeter of Old garden = (12w + 16)/2
Perimeter of Old garden = 6w + 8
Answer : The expression for the perimeter of old garden is 6w + 8
