Answer:
[tex]2(3x + 4b ) = 6x + 8b[/tex]
A car traveled a distance of 195 miles in 390 minutes.What is the cars average rate in miles per minutes?A) 2 miles per minute b) 40 miles per minute c) 0.5 miles per minute d) 390 miles per minute
Given data
Distance = 195 miles
Time = 390 minutes
[tex]\begin{gathered} \text{Average sp}eed\text{ = }\frac{Dis\tan ce}{\text{Time}} \\ =\text{ }\frac{195}{390} \\ =0.5\text{ miles per minute} \end{gathered}[/tex]Write 62° 21´ 47´´ as a decimal to the nearest thousandth. 62.413°62.366°62.363°62.373°
The given number is °:
[tex]62\degree21^{\prime}47^{\doubleprime}[/tex]To write it as a decimal, start by placing the integer part the same, now to find the decimal part, let's take the minutes 21' and divide it by 60 (because there are 60 minutes in 1°):
[tex]\frac{21^{\prime}}{60}=0.35[/tex]Now, let's divide the seconds 47" by 3600 (because there are 3600 seconds in 1°):
[tex]\frac{47^{\doubleprime}}{3600}=0.013[/tex]Thus, the number is:
[tex]62\degree+0.35\degree+0.013\degree=62.363\degree[/tex]The height of the triangle is 3 feet less than twice its base. The area of the triangle is 52 ft2. What is the height of the triangle?
Given:
Base of triangle = b
Height of triangle, h, is 3 feet less than twice its base. This is expressed as:
h = 2b - 3
Area of triangle = 52 ft²
To find the height of the triangle, use the Area of a triangle formula below:
[tex]A=\frac{1}{2}bh[/tex]Thus, we have:
[tex]\begin{gathered} 52=\frac{1}{2}\times b\times(2b-3) \\ \\ 52=\frac{b(2b-3)}{2} \end{gathered}[/tex]Let's solve for the base, b:
[tex]\begin{gathered} 52=\frac{2b^2-3b}{2} \\ \\ Multiply\text{ both sides by 2:} \\ 52\times2=\frac{2b^2-3b}{2}\times2 \\ \\ 104=2b^2-3b \end{gathered}[/tex]Subtract 104 from both sides to equate to zero:
[tex]\begin{gathered} 2b^2-3b-104=104-104 \\ \\ 2b^2-3b-104=0 \end{gathered}[/tex]Factor the quadratic equation:
[tex](2b+13)(b-8)[/tex]Thus, we have:
[tex]\begin{gathered} (2b+13)\text{ = 0} \\ 2b\text{ + 13 = 0} \\ 2b=-13 \\ b=-\frac{13}{2} \\ \\ \\ (b-8)=0 \\ b=8 \end{gathered}[/tex]We have the possible values for b as:
b = - 13/2 and 8
Since the base can't be a negative value, let's take the positive value.
Therefore, the base of the triangle, b = 8 feet
To find the height, substitute b for 8 from the height equation, h=2b-3
Thus,
h = 2b - 3
h = 2(8) - 3
h = 16 - 3
h = 13 feet.
Therefore, the height of the triangle, h = 13 feet
ANSWER:
13 feet
It is a Algebra problemSuppose an object is thrown upward with an initial velocity of 48 feet per second from a height of 120 feet. The height of the object t seconds after it is thrown is given by h(t)=-16t²+48t+120. Find the average velocity in the first two seconds after the object is thrown.
Answer
Average velocity in the first 2 seconds = 16 ft/s
Explanation
The average value of a function over an interval [a, b] is given as
[tex]\text{Average value of the function = }\frac{1}{b-a}\int ^b_af(x)dx[/tex]The integral is evaluated over the same interval [a, b]
Since we are asked to find the average velocity over the first 2 seconds, we need to first obtain the funcion for th object's velocity.
Velocity = (dh/dt)
h(t)= -16t² + 48t + 120
Velocity = (dh/dt) = -32t + 48
So, we can then find the average velocity over the first 2 seconds, that is, [0, 2]
[tex]\begin{gathered} \text{Average value of the function = }\frac{1}{b-a}\int ^b_af(t)dt \\ a=0,b=2,f(t)=-32t+48 \\ \text{Average Velocity = }\frac{1}{2-0}\int ^2_0(-32t+48)dt \\ =\frac{1}{2}\lbrack-16t^2+48t\rbrack^{2_{}}_0 \\ =\frac{1}{2}\lbrack-16(2^2)+48(2)\rbrack_{} \\ =0.5\lbrack-16(4)+96\rbrack \\ =0.5\lbrack-64+96\rbrack \\ =0.5\lbrack32\rbrack \\ =16\text{ ft/s} \end{gathered}[/tex]Hope this Helps!!!
The survey found that women's Heights are normally distributed with a mean of 63.9 in and standard deviation 2.2 in the survey also found that men's Heights are normally distributed with mean 67.6 in. and standard deviation 3.5 in considered and executed jet that seats 6 with a doorway height of 56.4 in. a)what percentage of adult men can fit through the door without bending?b) what's a doorway height would allow 40% of men to fit without bending
Let's begin by listing out the information given to us:
Mean for women (w) = 63.9 in
standard deviation for women (sd) = 2.2 in
Mean for men (m) = 67.6 in
standard deviation for men (sd) = 3.5 in
Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence how can Mia figure out how much more she has left to paint
If Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence then she 1380 more she has left to paint
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Mia is painting a fence that is 1625 meters long
Morning she painted 245 meter of the fence
We need to find how much more she has left to paint
To find this we need to subtract 245 from 1625
1625-245
1380
Hence 1380 more she has left to paint
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Simplity the expression:4b+9b
Since both variables are equal (b) we can add them:
[tex]4b+9b[/tex][tex]13b[/tex]If I can read 1,042 words in 5 minutes. What is my reading rate in words per minute?Round your answer to the nearest whole number.
ou are making identical door prizes for a charity event. You want to use all of the following items.
54 packages of peanuts
81 fruit bars
18 CDs
You can make at most
door prizes. Each door prize would have
packages of peanuts
fruit bars, and CDs
Putting the important informations, we want to use all items and divide them into equal groups in a way that we get the most prizes.
We we want a factor that is common to the three quantities, 54, 81 and 18, and is the greatest of them.
This is a question of Greatest Common Factor or Greatest Common Divisor (different names, same thing).
To calculate it, we have to find all the common factors of theses numbers.
One way to do that is to look for numbers that can divide all of them.
The numbers are 54, 81 and 18. As we can see the three numbers are divisable by 3:
[tex]\begin{gathered} \frac{54}{3}=18 \\ \frac{81}{3}=27 \\ \frac{18}{3}=6 \end{gathered}[/tex]So, we now that 3 is a common factor. Let's note it to use later on.
Now have got 18, 27 and 6. We can see that, again, all of them are divisable by 3:
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{27}{3}=9 \\ \frac{6}{3}=2 \end{gathered}[/tex]And let's note the "3" again to use later on.
The numbers now are 6, 9 and 2. 2 is only divisable by 2, but 9 isn't, so we don't have any more common factors.
In the end, we have the factor 3 and 3, which makes 3*3 = 9. Thus, 9 is the Greates Common Factor of 54, 81 and 18 and it divides them into 6, 9 and 2.
These are the answers we are looking for, because now we know that the most groups we can divide the items into is 9 and each group will have 6, 9 and 2 of those items.
So the phrase of the answer is:
"You can make at most 9 door prizes. Each door prize would have 6 packages of peanuts, 9 fruit bars, and 2 CDs."
Find the first three terms and stated term given the geometric sequence, with a1 as the first term. Given termsan=3^n-1, a5
Answer:
First three terms: 1, 3 and 9
Stated term = 81
Explanation:
Given the formula;
[tex]a_n=3^{n-1}[/tex]Let's go ahead and determine the first three terms of the geometric sequence.
For the 1st term;
[tex]\begin{gathered} a_1=3^{1-1} \\ =3^0 \\ =1 \end{gathered}[/tex]For the 2nd term;
[tex]\begin{gathered} a_2=3^{2-1} \\ =3^1 \\ =3 \end{gathered}[/tex]For the 3rd term;
[tex]\begin{gathered} a_3=3^{3-1} \\ =3^2 \\ =9 \end{gathered}[/tex]Let's now find the stated term;
[tex]\begin{gathered} a_5=3^{5-1} \\ =3^4 \\ =81 \end{gathered}[/tex]A rectangle has a width of 50 centimeters and a perimeter of 208 centimeters. What is the rectangle's length?The length is cm.
The perimeter of a plane figure is the distance around it.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the information given,
Perimeter = 208 cm, Width = 50 cm
Therefore,
208 = 2(length + 50)
By dividing both sides of the equation by 2, it becomes
104 = length + 50
length = 104 - 50
length = 54 cm
Length of rectangle is 54 cm
Juan's office had already recycled 24 kilograms this year before starting the new recycling
plan, and the new plan will have the office recycling 1 kilogram of paper each week. After
16 weeks, how many kilograms of paper will Juan's office have recycled?
kilograms
Answer:
40kg
24+16=40kg
Here is a linear equation: y=1/4x+5/41. Are (1, 1.5) and (12,4) solutions to the equation?A. Both (1, 1.5) and (12,4) are solutions to the equation.B. Neither (1, 1.5) and (12,4) are solutions to the equation.C. (1, 1.5) is a solution but (12,4) is not.D. (12,4) is a solution to the equation but (1, 1.5) is not.Explain your reasoning.3. Find the x-intercept of the graph of the equationExplain or show your reasoning.
To find if any given point is a solution for the linear equation, simply plug in the x and y values given and check if the equality stands, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (1,1.5) \\ \rightarrow1.5=\frac{1}{4}(1)+\frac{5}{4}\rightarrow1.5=\frac{6}{4}\rightarrow1.5=1.5✅ \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (12,4) \\ \rightarrow4=\frac{1}{4}(12)+\frac{5}{4}\rightarrow4=3+\frac{5}{4}\rightarrow4=4.25✘ \end{gathered}[/tex]Thereby the answer is:
C. (1, 1.5) is a solution but (12, 4) is not
Now, to find the x-intercept just make y = 0 and clear x, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ \rightarrow0=\frac{1}{4}x+\frac{5}{4}\rightarrow0=\frac{x+5}{4}\rightarrow0=x+5\rightarrow-5=x \\ \rightarrow x=-5 \end{gathered}[/tex]Therefore, the x-intercept is -5
I need help figuring out the answer to the m2
The area of the composite figure can be solved by separating the figure into 3 portions, which are 2 identical rectangles with one rectangle.
The image of the composite figure will be shown below
Let us sketch out the image of the two identical rectangles
The formula for the area(A) of a rectangle is,
[tex]A=length\times width[/tex]where,
[tex]\begin{gathered} l=length=5m \\ w=width=2m \end{gathered}[/tex]Therefore, the area(A1) of the two identical rectangles are
[tex]\begin{gathered} A_1=2\times(5\times2)=2\times5\times2=20m^2 \\ \therefore A_1=20m^2 \end{gathered}[/tex]Let me sketch the second rectangle
Therefore, the area(A2) will be
[tex]\begin{gathered} A_2=3\times2=6m^2 \\ \therefore A_2=6m^2 \end{gathered}[/tex]Hence, the area(A) of the composite figure is
[tex]\begin{gathered} A=A_1+A_2=20m^2+6m^2=26m^2 \\ \therefore A=26m^2 \end{gathered}[/tex]Therefore, the area is
[tex]26m^2[/tex]
Match each ratio of the volumes of two solids to the pair of solids it represents. 3 : 1 2r : 3h h : 4r 4r : h 4r : 3h 4 : 1
Solution
[tex]\begin{gathered} \text{ Volume of a cylinder }=\pi r^2h \\ \\ \text{ Volume of a cone =}\frac{1}{3}\pi r^2h \\ \\ \text{ Volume of a sphere }=\frac{4}{3}\pi r^3 \\ \\ \text{ Volume of hemisphere }=\frac{2}{3}\pi r^3 \end{gathered}[/tex]For 1.
[tex]\frac{\text{ Volume of a cylinder}}{\text{ Volume of a cone}}=\frac{\pi r^2h}{\frac{1}{3}\pi r^2h}=\frac{1}{\frac{1}{3}}=\frac{3}{1}=3:1[/tex]For 2.
[tex]\frac{\text{ Volume of a sphere}}{\text{ Volume of a cylinder}}=\frac{\frac{4}{3}\pi r^3}{\pi r^2h}=\frac{4r}{3h}=4r:3h[/tex]For 3.
[tex]undefined[/tex]Graph the line that passes through the point: (-1,-4) and who's slope is -2
The equation of the line is y = -2x -6.
We have,
The line passes through the point (-1, -4)
The slope of the line is -2.
The equation of the line when it passes through the point [tex](x_{1} ,y_{1} )[/tex] and has slope m is given by
[tex]y -y_{1} =m(x -x_{1} )[/tex]
Now, putting these values in the general equation of the line, we get,
y - (-4) = -2[ x -(-1) ]
y +4 = -2 [ x +1 ]
y +4 = -2x -2
y +2x = -2 -4
y +2x = -6
y = -2x -6
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Drake prepared 50 kilograms of dough in 5 hours. How many hours did Drake work if he prepared 70 kilogramsof dough at the same rate
We will determine how many hours he took to prepare 70 Kg as follows:
[tex]h=\frac{70\cdot5}{50}\Rightarrow h=7[/tex]It took him 7 hours.
A mover brings a box up the stairs in 10 seconds. If he applied a force of 20 N over a distance 10 m on the box, calculate the power required for him to complete this action
Total work done is calculated as
[tex]\begin{gathered} \text{work}=\text{force}\times dis\tan ce \\ \text{ =20N}\times10m \\ \text{ =200 J} \end{gathered}[/tex]The power is calculated as ,
[tex]\begin{gathered} \text{Power}=\frac{work}{\text{time}} \\ \text{ =}\frac{\text{200 J}}{10\text{ sec}} \\ \text{ =20 W} \end{gathered}[/tex]ity is net ranges $% per ment plus a one time.
Answer
a) The equation that represents the amount to be paid to xinfinity for using the internet for m months is
f(m) = 75m + 50
b) If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.
Explanation
If the amount paid in total fir using the xinfinity internet for m months onths is f(m),
And xinfinity internet charges a $75 per month fee plus a one-time activation fee of $50.
a) So, if one really does use the xinfinity internet for m months, the total charge is
f(m) = (75 × m) + 50
f(m) = 75m + 50
b) If Jose uses the xinfinity internet for 10 months, we cam calculate how much he pays the xinfinity.
m = 10 months
f(m = 10) = 75 (10) + 50
= 750 + 50
= 800 dollars.
If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.
Hope this Helps!!!is f(m),
And
E Xº = MLLEN = 50° yº = LN = ܘ L +7cm → N
In this case, we have an isosceles triangle, in this kind of figures the height (segment that goes from the vertex E to the base) bisects the upper angle, then the angle
[tex]m=\frac{50}{2}=25[/tex]Then, the measure of the upper angle of the triangle formed to the left equals 25°, the height of the triangle forms a right angle with the base of the triangle, then the measure of the angle on the right (next to y°) equals 90°. The sum of the internal angles of a triangle always equals 180°, then we can formulate the following expression:
x° + 25° + 90° = 180°
x° + 115° = 180°
x° + 115° - 115° = 180° - 115°
x° = 65°
Then x° equals 65°
As mentioned, the height forms a right angle with the base of the triangle, then the measure of the angle y° equals 90°
The length of the side LN equals twice the length of the base of the left triangle, then we get:
LN = 2*7 = 14
Then, the length of LN equals 14 cm
The table shows the diameters in volume certain balls used for different sports. A bowling ball has an approximate volume of 5200 cm³ what is the best estimate for the diameter of a bowling ball
From the table, the value V = 5200 cm³ is between x = 21 cm and x = 22 cm.
Computing the average of the volumes associated to these x-values, we get:
V = (4,849.1 + 5,575.3)/2
V = 5212.2
which is near V = 5200 cm³. Then, the x-value related to V = 5200 cm³ is approximately the average between x = 21 and x = 22, that is:
x = (21 + 22)/2
x = 21.5 cm
wpn Learning. UIC 3. Solve by elimination. x + 2y = -7 x - 5y = 7 A. (-7,0) B. (-3, -2) C. (-2,-3) D. (0, -7)
x+2y=-7 ------> equation 1
x-5y=7 -------->equation 2
Change the signs in equation 2
x+2y=-7 ------> equation 1
-x+5y=-7 -------->equation 2
Add equation 1 and 2
x+2y=-7 ------> equation 1
-x+5y=-7 -------->equation 2
_________
7y=-14
y=-14/7
y=-2
Now substitute y=-2 in equation 1,
x+2(-2)=-7
x-4=-7
x=-7+4
x=-3
(x,y)=(-3,-2)
Option B is the correct answer.
Instructions: Find the missing side. Round your answer to the nearest tenth. х 38° 30 X =
Let us call the third angle in the triangle y
y = 180 - 90-38 = 52 degrees ( sum of angles in a triangle is 180 degrees)
using trigonometric ratio
[tex]\sin \text{ 52=}\frac{\text{opposite}}{\text{hypothenuse}}[/tex]opposite = x
hypothenuse = 30
[tex]\begin{gathered} \sin 52\text{ =}\frac{x}{30} \\ x=\text{ 23.64032261} \end{gathered}[/tex]To the nearest tenth x = 23.6
47 Dominic used the equation below to find d, the amount in dollars he would spend on gasolineto drive a distance of m miles.d =(3.5)Based on this equation, how much would Dominic spend on gasoline to drive a distance of180 miles?A $25.203.628B $21.00 - 2.94C $24.50 -343: 3.02D $28.00
Answer
Explanation
The equation that
I need help to find the area of each sector. I will send the exercise
The area of the circular sector is given by:
[tex]\begin{gathered} A=\frac{r^2\theta}{2} \\ where\colon \\ r=radius=17mi \\ \theta=angle=\frac{2\pi}{3} \\ \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=\frac{(17^2)\frac{2\pi}{3}}{2} \\ A=\frac{289\pi}{3}\approx302.64 \end{gathered}[/tex]A number is multiplied by 6 and the product is added to 4 the sum is equal to the product of 2 and 17 find the number
A number = x
Is multiplied by 6 = 6x
And the product is added to 4 = 6x + 4
The sum is equal to the product of 2 and 17 ; 6x + 4 = 2 * 17
Solve for x
6x + 4 = 2 * 17
Combine like terms
6x = 34 - 4
6x = 30
Divide both sides by 6
6x/6 = 30/6
x = 5
Answer:
5, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
the product of 2 and 17 is 34
34 - 4 is 30
30 devided by 6 is 5
therefore, by working backwords we can figure out that this math riddle would be equal to 5 ^^
A pizza restaurant has found that the probability that a customer will order thin crust is 0.4. In a random sample of 5 customers who order a pizza, find the probability that at least three of them want thin crust.
In this type of exercises, the probability of x successes on n reapeted trials in an experiment is given by the next formula:
[tex]P=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Here the nCx indicates the number of different combinations of x objects selected from a set of n objects. With the given data we can solve it easily:
p = 0.4
n = 5
x = 3
[tex]\begin{gathered} P=5\text{C3}\cdot0.4^3\cdot(1-0.4)^{5-3} \\ P=10\cdot0.064\cdot0.36 \\ P=0.2304 \end{gathered}[/tex]Perform the indicated operation.1.61 kg -200 g1.61 kg - 200 g-9 (Type [whole number or a decimal.)
Answer:
Explanation:
We are asked to subtract 200 g from 1.61 kg. To perform this operation, we first convert kg to grams.
Now,
1 kg = 1000g
therefore,
1.61 kg = 1.61 * 1000 g = 1610 g.
The operation now becomes
1610 g - 200 g
which evaluates to
1610 g - 200 g = 1410 g
Which is our answer!
PLEASE ANSWER QUESTION 2(1.) The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. answer: 10 yards(2.)Is the value you just wrote for the total length of the walkway a rational or irrational number? Explain.
We need to compute the hypotenuse of 4 right triangles.
The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of the right triangle.
In one of the triangles, the length of the legs are: 6 and 8 yards. Then the length of the hypotenuse is:
[tex]\begin{gathered} c^2_1=6^2+8^2 \\ c^2_1=36+64 \\ c_1=\sqrt[]{100} \\ c_1=10yd_{} \end{gathered}[/tex]In another triangle, the length of the legs are: 12 and 8 yards. Then the length of the hypotenuse is:
[tex]\begin{gathered} c^2_2=12^2+8^2 \\ c^2_2=144+64 \\ c_2=\sqrt[]{208} \\ c_2=4\sqrt[]{13}\text{ yd} \end{gathered}[/tex]In the triangle whose hypotenuse (c3) is 15 yd and one of its legs is 12 yd, the unknown is one of the legs, b, which can be computed as follows:
[tex]\begin{gathered} 15^2=12^2+b^2 \\ 225=144+b^2 \\ 225-144=b^2 \\ \sqrt[]{81}=b \\ 9=b \end{gathered}[/tex]The last triangle has legs of 9 yd and 6 yd. Its hypotenuse is:
[tex]\begin{gathered} c^2_4=9^2+6^2 \\ c^2_4=81+36 \\ c_4=\sqrt[]{117} \\ c_4=3\sqrt[]{13} \end{gathered}[/tex]Finally, the length of the walkway is:
[tex]\begin{gathered} c_1+c_2+c_3+c_4=10+4\sqrt[]{13}+15+3\sqrt[]{13}= \\ =(10+25)+(4\sqrt[]{13}+3\sqrt[]{13})= \\ =35+7\sqrt[]{13} \end{gathered}[/tex]This value is irrational because it includes and square root
Thaddeus models the number of hours of daylight in his townas
We have the following function
[tex]D(t)=2.5\sin\frac{\pi t}{6}+12[/tex]The maximum and minimum of that function happens when sin(x) = 1 or sin(x) = -1, respectively.
Then let's find the maximum, that happens when the sin value is 1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot1+12 \\ \\ D(t)=2.5+12 \\ \\ D(t)=14.5 \end{gathered}[/tex]And the minimum, when sin value is -1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot(-1)+12 \\ \\ D(t)=-2.5+12 \\ \\ D(t)=9.5 \end{gathered}[/tex]Then the least: 9.5 hours; greatest: 14.5 hours.