Answer:
$35.5
Explanation:
If Bobby purchased 15 gallons of gas and each gallon cost $2.25, the total cost of the gallons of gas is:
15 x $2.25 = $33.75
Adittionally, Bobby bought a soda for $1.75, so he spend a total of:
$33.75 + $1.75 = $35.5
So, he spends $35.5
Consider the equation cos(2t) = 0.8. Find the smallest positive solution in radians and round your answer to 2 decimal places.
Given:
cos(2t) = 0.8
Take the cos⁻' of both-side of the equation.
cos⁻' cos(2t) = cos⁻'(0.8)
2t = cos⁻'(0.8)
Calculate the value of the right- hand side with your calculator in radians.
2t =0.6435
Divide both-side of the equation by 2
t ≈ 0.32
an environmental scientists is conducting research on a particular type of air pollutant. She collects air samples over time and determines the average number of micrograms (ug) of the pollutant in a cubic meter (m^3). Her data are shown in the table below.Which Function models the scientists data?A. F(×)=1.12t +50B. F(×)=50 · 1.12tC. F(×)=50 - 6tD. F(×)=50 · 0.88^t
If we graph the points of the table in a coordinate system we'll see that they line up like a line function, so option D is not possible.
If we also add the graphs for the other 3 options, we get:
The points don't line up perfectly but they are much closer to the line in blue than the red or black lines.
Therefore answer is option C f(t) = 50 - 6t
I'm trying to simplify negative 5/8 divided by negative 3/4 how do I do that?
x+y+z=12x+4y+2z = -6-x+9y-3z=-49 Can someone please help me solve this system of equation?
Let's begin by listing out the information given to us:
[tex]\begin{gathered} x+y+z=1 \\ 2x+4y+2z=-6 \\ -x+9y-3z=-49 \end{gathered}[/tex]To solve this 3 variable equation, let's eliminate one of the variables
add equation 1 & 3, we have:
[tex]\begin{gathered} x-x+y+9y+z-3z=1-49 \\ 10y-2z=-48 \\ Make\text{ z the }subject,we\text{ have:} \\ -2z=-10y-48 \\ divide\text{ through by -2} \\ z=5y+24 \end{gathered}[/tex]Substitute z into equation 1, 2 & 3
[tex]\begin{gathered} x+y+5y+24=1 \\ x+6y=1-24 \\ x+6y=-23 \end{gathered}[/tex][tex]\begin{gathered} 2x+4y+2\left(5y+24\right)=-6 \\ 2x+4y+10y+48=-6 \\ 2x+14y=-6-48 \\ 2x+14y=-54 \end{gathered}[/tex][tex]\begin{gathered} -x+9y-3\left(5y+24\right)=-49 \\ -x+9y-15y-72=-49 \\ -x-6y=-49+72 \\ -x-6y=23 \end{gathered}[/tex]Solve as a simultaneous equation, we have:
[tex]\begin{gathered} x+6y=-23 \\ 2x+14y=-54 \\ \text{Multiply the top equation by 2 \& subtract it from the bottom equation} \\ 2\cdot(x+6y=-23)\Rightarrow2x+12y=-46 \\ 2x+14y=-54-(2x+12y=-46) \\ 2x-2x+14y-12y=-54-(-46) \\ 2y=-8 \\ y=-4 \end{gathered}[/tex]Substitute y = -4 into x + 6y = -23, we have:
[tex]\begin{gathered} x+6\left(-4\right)=-23 \\ x-24=-23 \\ x=-23+24 \\ x=1 \end{gathered}[/tex]Substitute y = -4 into z = 5y + 24, we have:
[tex]\begin{gathered} z=5\left(-4\right)+24 \\ z=-20+24 \\ z=4 \end{gathered}[/tex]Khalil has 2 1/2 hours to finish 3 assignments if he divides his time evenly , how many hours can he give to each
In order to determine the time Khalil can give to each assignment, just divide the total time 2 1/2 between 3 as follow:
Write the mixed number as a fraction:
[tex]2\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}[/tex]Next, divide the previous result by 3:
[tex]\frac{\frac{5}{2}}{\frac{3}{1}}=\frac{5\cdot1}{2\cdot3}=\frac{5}{6}[/tex]Hence, the time Khalil can give to each assignment is 5/6 of an hour.
A focus group of 12 people is to be chosen randomly from among 24 right-handed people and 5 left-handed people. In order to find the probability that 3 of the people chosen are right-handed, you should use
Let 1 and 2 mean that a person is right-handed or left-handed, respectively.
Consider the probability space as the different groups of 12 people that can be formed with the 29 total people. {(1,1,1,1,1,...1),(2,1,1,1,1,...,1),...}
We need to use the binomial distribution in order to find the answer.
Consider X to be the number of right-handed people in the group.
The probability of X=3 is then:
[tex]Pr(X=3)=\text{ binomial coefficien(}12,3\text{)}(\frac{24}{29})^3(1-\frac{24}{29})^{12-3}[/tex]We used the formula
[tex]\begin{gathered} Pr(X=k)=\text{ binomial coefficient(n,k)}\cdot p^k(1-p)^{n-k} \\ \text{where } \\ k=3 \\ n=12 \\ p=\frac{24}{29} \end{gathered}[/tex]Finally, we need to simplify the expression, as shown below
[tex]\Rightarrow P(X=3)=220(\frac{24}{29})^3(\frac{5}{29})^9=0.0000167[/tex]This is the answer one obtains using the binomial distribution; nevertheless, the actual probability is equal to zero because it is not possible to form a group of 12 people that only contains 3 right-handed people as there are only 5 left-handed people (3+5=8).
5000 + 300 + 8 in standard form
The given arithmetic expression is:
5000 + 300 + 8
This sum can be computed as shown below:
Therefore, 5000 + 300 + 8 = 5308
Convert 5308 to standard form
[tex]5308\text{ = 5.308 }\times10^3[/tex]
11. (04.02 LC) Saving all the money in a safe at home most likely means (5 points) being stingy being dishonest being untrusting O being thrifty
Saving all the money in a safe at home most likely means D. being thrifty
What is money?Money is any commodity or verifiable record that is widely accepted in a given country or socioeconomic environment as payment for products and services and repayment of debts, such as taxes.
Money enables us to meet our most basic requirements, such as purchasing food and shelter and paying for healthcare. Meeting these demands is critical, and if we don't have enough money to do so, our personal well-being and the community's overall well-being suffer considerably.
In this case, saving the money means that the person is careful with spending and doesn't want to waste the money. This implies thrifty.
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Answer:
Being thrifty
Simplify the expression -3n-8-7n + 17
We simplify by combining like terms
therefore
[tex]\begin{gathered} -3n-8-7n+17 \\ =-3n-7n-8+17 \\ =-10n+9 \end{gathered}[/tex]5. Infer from the problem: What is the y-intercept of the line y=3x-5 ?
the given expression is
y = 3x - 5
y +5 = 3x
y - (-5) = 3(x - 0)
so the y-intercept is -5.
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43524
[tex]\frac{d32423657565\mod{43242}}{dx}_{564564}[/tex]4tet
54
Passing through (- 4,-7) and (1,3) What is the equation of the line in point-slope form
To calculate the equation of the line passing through the points ( -4. -7) and (1, 3):
[tex]\begin{gathered} \text{ Equation of the line can be calculated by the formula } \\ y-y_1=m(x-x_1) \end{gathered}[/tex]where m = slope
(x1, y1) = any of the points given; say points (-4, -7). That is x1= -4, y1 = -7
To calculate the slope, m:
[tex]\begin{gathered} \text{ m = }\frac{y_2-y_{1_{}}}{x_2-x_1}_{} \\ \text{ where }(x_2,y_2)\text{ = (1, 3)} \\ m\text{ = }\frac{3\text{ - (-7)}}{1-(-4)} \\ m=\text{ }\frac{3+7}{1+4}\text{ = }\frac{10}{5} \\ m=2 \end{gathered}[/tex][tex]\begin{gathered} \text{ substituting m = 2, x}_1=-4,y_1=-7\text{ into the formula }y-y_1=m(x-x_1) \\ we\text{ have} \\ y-(-7)=2(x-(-4)\text{ )} \\ y+7=\text{ 2(x+ 4)} \end{gathered}[/tex]The equation of the line in point slope form is y + 7 = 2(x + 4)
20g of radioactive substance decays by 1/2 of it's original
amount every 30 days. How much is left after 10 days.
The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Radioactive decays by 1/2 of its original in 30 days.
1/2 of original → 30 days.
Divide both sides by 3
1/6 of original → 10 days
Therefore, in 10 days amount of decays will be,
1/6 of 20 ⇒ 20/6 = 3.33
The amount left = 20 - 3.33 = 16.67.
Hence "The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g".
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Factor 12x² + 19x - 21.O (6x + 7)(2x − 3)—O (4x - 3)(3x + 7)O(6x-7)(2x + 3)(4x + 3)(3x7)
given the expression
[tex]12x^2+19x-21[/tex]we are loking 2 numbers whose multiplication is equal to 12
and other 2 number whose multiplication is equal to 21
the sum of the cross multiplication is equal of 19, as follows
[tex](4x*3x)+((4x*7)+(3x*-3))+(-3*7)[/tex]factor is
[tex]\left(4x-3\right)\left(3x+7\right)[/tex]correct answer option B
distribute and simply 5(3x+1)-6x
A landscaper has built a U-shaped raised bed in a vegetable garden as shown in the figure. How many cubic yards of soil should be ordered to fill the bed to a depth of 30 inches?
First calculate the area of the shaded region by considering the U-shaped bed as formed by three rectangles, as follow:
where the lengths of the sides of the rectangles corresponds with the dimensions of the U-shaped bed.
Then, for the area of the figure, use the formula for the area of a rectangle, for all three rectangles, as follow:
A = 5*18 + 3*20 + 5*18
A = 90 + 60 + 90
A = 240
Then, the area is 240 in^2
Next, convert the previous result to yd^2. Use the equivalence 1 yd = 36 in:
[tex]240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2[/tex]Now, to find the volume convert 30 in to yards:
[tex]30in\cdot\frac{1yd}{36in}=0.83yd[/tex]Finally, multiply the previous result by the area of the figure:
[tex]0.185yd^2\cdot0.83yd=0.154yd^3[/tex]What is the reference angle for 289°? A. 71° B. 19° C. 11° D. 89°
Given:
Angle θ=289°.
For angles from 270° to 360°, the reference angle can be calculated by subtracting the given angle from 360° .
The reference angle of θ can be calculated as:
[tex]\begin{gathered} 360\degree-\theta=360\degree-289\degree \\ =71\degree \end{gathered}[/tex]Therefore, reference angle of 289° is 71°.
Consider the triangles ADB and EDC. Explain how they are similar.
Example: Triangles like ABC and EDC are similar by SAS similarity, because angle C is congruent in each triangle, and AC/EC = BC/DC = 2. By the definition of similarity, it follows that AB/DE = BC/EF = AC/DF = 2.
Which expression is equivalent to 8C +6 minus 3c minus 2
To simplify the expression above, simply combine similar terms.
The similar terms in the expression above are 8c and -3c as well as 6 and -2.
Let's combine the pairs of similar terms.
[tex](8c-3c)+(6-2)[/tex]So, 8c - 3c = 5c and 6 - 2 = 4. Hence, the answer is:
[tex]5c+4[/tex]The answer is 5c + 4. (Option A)
The Ferris wheelThe community loves the Ferris Wheel because when they are at the top of the wheel they can look for their house and it has long been a family favorite. The company sent you a Ferris wheel that has a radius of 40 ft. and each car is 5 ft. tall. The people can’t start to look for their houses until they get above the tents of the carnival and those tents are 20ft tall. The Ferris wheel has 20 passenger cars and it takes 12 minutes to have all the cars filled. Once all cars are filled the Ferris wheel runs at 1 rotation for every 2 minutes for a total of 8 minutes.Once someone has boarded the Ferris wheel, how long will it take for them to be able to start looking for their house?How long will they have to search for their house?
Given:
radius of Ferris wheel = 40 ft
height of a car = 5 ft
height of a tent = 20 ft
no. of passenger cars = 20
time to load all cars = 12 minutes
time for 1 rotation = 2 minutes
time for all rotations = 8 minutes
What we want to know is how many degrees the car will have to travel along the circle before it reaches a height of 20 ft.
We can draw a triangle to represent the unknown and find the angle.
The total height from the ground to the center of the Ferris wheel is 45 ft (5ft car height + 40 ft radius). We deduct the 20ft height of the tent so we get the side of the right triangle we're using to solve for the missing angle. That height is 25 ft.
The radius also serves as the hypotenuse of the triangle.
We can then use the following to solve for the angle theta:
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \\ \cos\theta=\frac{25}{40} \\ \\ \cos^{-1}(\cos\theta)=\cos^{-1}(\frac{25}{40}) \\ \\ \theta=51.3\degree \end{gathered}[/tex]Now we know that the car must travel 51.3 degrees along the circle before it gets to a height where it can see above the tents. If one rotation is 360 degrees and it takes 2 minutes to complete one round, then to find the time it will take to travel 51.3 degrees, we use the following equation:
[tex]\begin{gathered} \frac{360\degree}{2minutes}=\frac{51.3\degree}{x\text{ }minutes} \\ \\ x=\frac{51.3(2)}{360} \\ \\ x=0.285\text{ minutes or }17.1\text{ seconds} \end{gathered}[/tex]It will take them 17.1 to be able to start looking for their house.
Now every time the car goes around the path of the Ferris wheel, for 17.1 going up and another 17.1 seconds going down, they will not be able to look for their house.
17.1 seconds x 2 x 4 turns = 136.8 seconds
8 minutes - 136.8 seconds = 480 - 136.8 = 343.2 seconds or 5 minutes and 43.2 seconds
They have 5 minutes and 43.2 seconds to look for their house.
Slope The first two sets of points are 9,-24 and 13,-21
We need to find the slope using the points (9, -24) and (13 , -21)
so, the slope = 3/4
A pancake recipe asked for one and 2/3 times as much milk as flower if two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Let x be the quantity of flour used
Let y be the quantity of milk used
A pancake recipe asked for one and 2/3 times as much milk as flour:
[tex]y=1\frac{2}{3}x[/tex]If two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Find x when y=2 1/2:
[tex]2\frac{1}{2}=1\frac{2}{3}x[/tex]Write the quantities as fractions;
[tex]\begin{gathered} 2+\frac{1}{2}=(1+\frac{2}{3})x \\ \\ \frac{4}{2}+\frac{1}{2}=(\frac{3}{3}+\frac{2}{3})x \\ \\ \frac{5}{2}=\frac{5}{3}x \end{gathered}[/tex]Solve x:
[tex]x=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{15}{10}[/tex]Write the answer as a mixed number:
[tex]\frac{15}{10}=\frac{10}{10}+\frac{5}{10}=1+\frac{5}{10}=1+\frac{1}{2}=1\frac{1}{2}[/tex]Then, for 2 1/2 cups of milk would be needed 1 1/2 cups of flourAnswer: 1 1/2In the matrix equation below, what are the values of x and y? 1/2 [4 8 x+3 -4] -3 [1 y+1 -1 -2]= [-1 -5 7 4]
Using the matrix equation, the value of x and y are 5 and 2 respectively.
Consider the 2 by 2 matrix equations,
1/2 [ 4 8 ( x + 3 ) - 4 ] - 3[ 1 y+1 -1 - 2 ] = [ - 1 -5 7 4 ]
[ 2 4 (x+3)/2 -2] + [ - 3 -3y -3 +3 + 6] = [ - 1 - 5 7 4]
[ -1 -3y + 1 (x + 9)/2 + 4] = [ - 1 - 5 7 4]
Therefore,
- 3y + 1 = - 5
Subtracting 1 from each side of the equation,
- 3y + 1 - 1 = - 5 - 1
- 3y = - 6
Dividing each side of the equation by - 3,
y = 2
And;
( x + 9 )/2 = 7
Multiplying each side by 2,
x + 9 = 14
Subtracting 9 from each side of the equation,
x + 9 - 9 = 14 - 9
x = 5
Therefore, the value of x and y is 5 and 2 respectively.
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Exact value of tan 2pi/3
Given:
[tex]\tan\frac{2\pi}{3}[/tex]Find-:
Exact value
Explanation -
So, the value is:
[tex]=\tan\frac{2\pi}{3}[/tex][tex]\begin{gathered} =\tan\frac{2\pi}{3} \\ \\ \pi=180\text{ then,} \\ \\ =\tan(\frac{2\times180}{3}) \\ \\ =\tan(120) \end{gathered}[/tex]So value is:
[tex]\tan(120)=-\sqrt{3}[/tex]the figure below has a point marked with a large. First translate to figure 4 units up then give the coordinates of the mark point in the original figure in the final figure.:
Large point coordinates (original)= (1,-4)
To obtain the coordinates of the new point, add 4 to the y coordinate.
(1,-4+4) = (1,0)
Drag the tiles to the boxes to form correct pairs.Match each operation involving fx) and g(x) to its answer.(T) = 1 - 22 and g(x) = V11 – 40(gx )(2)(8 - 1)(-1)(9 + )(2)-373V3 - 30V15
1.
[tex](g\times f)(2)[/tex]It means multiply f(x) and g(x) and then put "2" into it. The solution is what we are looking for. So,
[tex]\begin{gathered} (g\times f)(2)=\sqrt[]{11-4x}\times1-x^2 \\ =\sqrt[]{11-4(2)}\times1-(2)^2 \\ =\sqrt[]{3}\times-3 \\ =-3\sqrt[]{3} \end{gathered}[/tex]2.
[tex](g-f)(-1)[/tex]For this we subtract f from g and put -1 into the expression. So
[tex]\begin{gathered} (g-f)(-1)=\sqrt[]{11-4x}-1+x^2 \\ =\sqrt[]{11-4(-1)}-1+(-1)^2 \\ =\sqrt[]{15}-1+1 \\ =\sqrt[]{15} \end{gathered}[/tex]3.
[tex](g+f)(2)[/tex]We simply add f and g and put 2 into the final expression.
[tex]\begin{gathered} (g+f)(2)=\sqrt[]{11-4x}+1-x^2 \\ =\sqrt[]{11-4(2)}+1-(2)^2 \\ =\sqrt[]{3}-3 \end{gathered}[/tex]4.
[tex]\begin{gathered} (\frac{f}{g})(-1) \\ \end{gathered}[/tex]We divide f by g and put -1 in the final expression. Shown below:
[tex]\begin{gathered} (\frac{f}{g})(-1)=\frac{1-x^2}{\sqrt[]{11-4x}} \\ =\frac{1-(-1)^2}{\sqrt[]{11-4(-1)}} \\ =\frac{0}{\sqrt[]{15}} \\ =0 \end{gathered}[/tex]Now, please match each answer with each choice.
What’s eight less than four times a number in algebraic expression
Answer:
4x - 8, 4x just means four of x, and eight less means to subtract 8.
Step-by-step explanation:
Answer:
The answer is 4x - 8 and it equals -32
solve the following equation for pp/r+s=q
the initial equation is:
[tex]\frac{p}{r}+s=q[/tex]To solve for p we can rest s in bout sides so:
[tex]\begin{gathered} \frac{p}{r}+s-s=q-s \\ \frac{p}{r}=q-s \end{gathered}[/tex]Now we can multiply by r so:
[tex]\begin{gathered} \frac{p\cdot r}{r}=(q-s)\cdot r \\ p=(q-s)\cdot r \end{gathered}[/tex]Write an equation for the inverse variation represented by the table.x -3, -1, 1/2, 2/3y 4, 12, -24, -18
By definition, Inverse variation equations have the following form:
[tex]y=\frac{k}{x}[/tex]Where "k" is the Constant of variation.
Given the values shown in the table, you can find the value of "k":
- Choose a point from the table. This could be:
[tex](-3,4)[/tex]Notice that:
[tex]\begin{gathered} x=-3 \\ y=4 \end{gathered}[/tex]- Substitute these values into the equation and solve for "k":
[tex]\begin{gathered} 4=\frac{k}{-3} \\ \\ (4)(-3)=k \\ k=-12 \end{gathered}[/tex]Knowing the Constant of variation, you can write the following equation:
[tex]y=\frac{-12}{x}[/tex]The answer is:
[tex]y=\frac{-12}{x}[/tex]Please help with #4. The directions are with the pic below.
sphere: 12 pounds
cylinder: 108 pounds
Explanation:
Data:
. From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
. From balance B:
3 cubes = 5 spheres
Since 1 cube = 20 pounds
=> From balance B:
3 cubes * 20 pounds = 5 spheres
60 pounds = 5 sphere
60 / 5 = 5 / 5
12 pounds = 1 sphere
=> From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
3 spheres * 20 pounds + 1 sphere * 12 pounds = 1 cylinder + 2 spheres * 12 pounds
120 pounds + 12 pounds = 1 cylinder + 24 pounds
132 pounds = 1 cylinder + 24 pounds
132 pounds - 24 pounds = 1 cylinder + 24 pounds - 24 pounds
108 pounds = 1 cylinder
