Given:
The cost of tortilla chips = 35.5 cents per ounce
The bag of tortilla chips = $4.63 = 463 cents
To find the number of ounces in the bag, divide 463 by 35.5
so,
The number of ounces =
[tex]\frac{463}{35.5}=13.04225[/tex]Rounding to the nearest hundredth
so, the answer will be 13.04 ounces
A baseball is hit, following a path represented by x = 130t and y = 3.2 + 42t − 16t 2 for 0 ≤ t ≤ 3.
Part A)
Evaluate x(t) and y(t) at t=0.2, 1.2 and 2.4 to find the ordered pairs.
[tex]\begin{gathered} x=130t \\ y=3.2+42t-16t^2 \end{gathered}[/tex]t=0.2
[tex]\begin{gathered} x=130\times0.2=26 \\ y=3.2+42\times0.2-16\times0.2^2=10.96 \end{gathered}[/tex]Then, the ordered pair for t=0.2 is (26,10.96).
t=1.2
[tex]\begin{gathered} x=130\times1.2=156 \\ y=3.2+42\times1.2-16\times1.2^2=30.56 \end{gathered}[/tex]Then, the ordered pair for t=0.2 is (156,30.56).
t=2.4
[tex]\begin{gathered} x=130\times2.4=312 \\ y=3.2+42\times2.4-16\times2.4^2=11.84 \end{gathered}[/tex]Then, the ordered pair for t=2.4 is (312,11.84).
Part B)
Find a rectangular equation (y as a function of x) to find the height of the ball when it reaches a horizontal distance of 320ft. To do so, isolate t from the equation for x:
[tex]\begin{gathered} x=130t \\ \Rightarrow t=\frac{x}{130} \end{gathered}[/tex]Replace t=x/130 into the equation for y:
[tex]\begin{gathered} y=3.2+42t-16t^2 \\ \Rightarrow y=3.2+42(\frac{x}{130})-16(\frac{x}{130})^2 \\ \Rightarrow y=3.2+\frac{42}{130}x-16\times\frac{x^2}{16,900} \\ \Rightarrow y=3.2+\frac{42}{130}x-\frac{16}{16,900}x^2 \\ \Rightarrow y=3.2+\frac{42}{130}x-\frac{4}{4,225}x^2 \end{gathered}[/tex]Replace x=320 to find the height of the ball:
[tex]y=3.2+\frac{42}{130}(320)-\frac{4}{4225}(320)^2=9.6378...[/tex]Since the height of the ball is less than the height of the fence when it reaches a horizontal distance of 320ft, then the baseball doesn't travel over the fence.
Part C)
A rectangular equation to represent the plane curved was already found in Part B:
[tex]y=3.2+\frac{42}{130}x-\frac{4}{4225}x^2[/tex]hello could you please tell me if I have selected the right answer?
we need to reduce
[tex]\frac{-28x^2y}{7xy^2}[/tex]this can be computed as
[tex](-\frac{28}{7})(\frac{x^2}{x})(\frac{y}{y^2})[/tex]hence, we have
[tex](-4)(x)(\frac{1}{y})[/tex]which is equal to
[tex]\frac{-4x}{y}[/tex]for a new problem, ou must start a new session (Brainly rules). One question per session helps you to find the question at anytime and helps other students to find the answer for the same question.
The question and data are below. I put this as chemistry but a chemist could not answer it because it is constructing a graph with data provided. I think it fits into the mathematics option so I put it here :)) thx for the help by the way.
SOLUTION:
First we plot the graph of Temp vs Volume of air
Part A)Using desmos online graphing tool, the above is obtained as regression
[tex]\begin{gathered} y=\text{ 0.0154625x + 4.63602} \\ \text{hence, because x represents volume, when x=0} \\ y=\text{ 4.63602}\degree C^{} \end{gathered}[/tex]First we plot the graph of Temp vs Volume of (N2/H2/He)
Is the triangle with the vertices A(7,3), B(0,7), and C(-8, -7) a right triangle?Is the triangle a right triangle?O YesO No
Solution
We want to use coordinate geometry to determine if the triangle is a right triangle
We can find the distance between all the three vertices.
The formula for distance between two points ( x1 , y1 ) and ( x2, y2) is given as :
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Let us start by finding the distance AB
Let us find the distance BC
Now let us find the distance AC
The triangle will be a right triangle if it obeys pythagoras theorem
Pythagoras' theorem says if we square the longest side in a right triangle , then it must be equal to the sum of the squares of the other two sides
Let us see if that works. If it works, the triangle is right triangle. If it doesn't work, we conclude otherwise.
So we can say that only right triangle obeys pythagoras' theorem.
Now lets verify
Longest side is AC
[tex]AC=5\sqrt{13}[/tex][tex]\begin{gathered} AC^2=(5\sqrt{13)^2}=\text{ }5\sqrt{13}\times5\sqrt{13}=325 \\ AC^2=325 \end{gathered}[/tex]
Let us find the sum of the squares of AB and BC
[tex]\begin{gathered} AB^2+BC^2=\sqrt{65^2}+(2\sqrt{65)}^2 \\ AB^2+BC^2=65+260=325 \end{gathered}[/tex]Now we observe that ;
[tex]AC^2=AB^2+BC^2[/tex]The triangle given is a right triangle
Our choice is Yes
A surveyor stands at a window on the 9th floor of an office tower. He measures the angles of elevation and depression of the top and the base of a taller building. The surveyor sketches this plan of his measurements. Determine the height of the taller building to the nearest tenth of a meter.
Given,
The height of the building upto 9th floor is 39 meters.
The angle of elevation is 31 degree.
The angle of depression is 42 degree.
The diagram of the building and taller building is,
Consider,
AB is the height of the building upto 9th floor.
CE is the height of the taller biulding.
BE=AD is the distance between building and taller building.
Taking triangle ADE,
[tex]\begin{gathered} \tan 42^{\circ}=\frac{DE}{AD} \\ \text{here, DE=AB=39m} \\ \tan 42^{\circ}=\frac{39}{AD} \\ AD=\frac{39}{\tan42^{\circ}} \\ =\frac{39}{0.900} \\ =43.34\text{ m} \end{gathered}[/tex]The distance between the building and the taller building is 43.34 m (approximately).
Taking triangle ADC,
[tex]\begin{gathered} \tan 31^{\circ}=\frac{CD}{AD} \\ \tan 31^{\circ}=\frac{CD}{43.34} \\ 0.601\times43.34=CD \\ CD=26.04734\text{ m} \\ \approx26.05\text{m} \end{gathered}[/tex]The height of the taller building is,
[tex]\text{Height of building =CD+DE=39+26.05=}65.05\approx65.1\text{ m}[/tex]The height of the taller building is 65.1 meter.
17. Which expressions contain exactly two terms? Choose ALL that is correct. A. -5 +6x +3y²B. 4xC. 7-9x D. (x + 2)(y - 4)E. 8x² + 5x
To be able to determine which among the expression contains exactly two terms, let's count how many terms each expression has.
A.) -5 +6x +3y²
The expression has the terms: -5, 6x and 3y²
Therefore, the total number of terms is 3.
B.) 4x
The expression has the terms: 4x
Therefore, the total number of terms is 1.
C.) 7-9x
The expression has the terms: 7 and -9x
Therefore, the total number of terms is 2.
D.) (x + 2)(y - 4)
Let's first expand the expression,
[tex]\mleft(x+2\mright)\mleft(y-4\mright)\text{ = xy -4x + 2y - 8}[/tex]The expression has the terms: xy, -4x, 2y and -8
Therefore, the total number of terms is 4.
E.) 8x² + 5x
The expression has the terms: 8x² and 5x
Therefore, the total number of terms is 2.
Conclusion: Only the expression at C and E contains exactly two terms.
Therefore, the answer is C and E.
3. The table shows the linear relationship between the balance of a student's savings account and the number of weeks she has been saving. Savings Account Week 0 1 2 4 7 12 Balance (dollars) 24 32 40 56 80 120 Based on the table, what was the rate of change of the balance of the student's savings account in dollars and cents per week?
The number of weeks are 0 1 2 4 7 12
The balances are 24 32 40 56 80 120
The rate of change of the balance of the student's savings account in dollars and cents per week is also referred to as the slope of the graph that can be potted with these values. The formula for slope is expressed as
Slope = (y2 - y1)/(x2 - x1)
y1 and y2 would be consecutive values of the balance
x1 and x2 would be consecutive values of the number of weeks
When x1 = 0, y1 = 24
When x2 = 1, y1 = 32
Slope = (32 - 24)/(1 - 0)
Slope = 8
The rate of change of the balance of the student's savings account in dollars and cents per week is 8 dollars per week. Converting to cents, it would be 800 cents per week
can you help me solve this?Identify the property being used
Solution
- The question asks us for which property is used in the following equation
[tex]2(RB)\cos \theta=2R(B\cos \theta)[/tex]- The question uses the Commutative Property of Multiplication.
- This property is stated below:
[tex]A(DC)=C(AD)[/tex]Final Answer
The answer is Commutative Property of Multiplication
1. you are fishing for trout and bass. gaming laws allow you to catch no more than 15 trout per day, no more than 10 bass per day, and no more than 20 total fish per day. can you catch 11 trout and 9 bass? why or why not?
toLet the number of trout = x
And the number of bass = y
gaming laws allow you to catch no more than 15 trout per day, no more than 10 basses per day.
So,
[tex]\begin{gathered} x\le15 \\ y\le10 \end{gathered}[/tex]And no more than 20 total fish per day
So,
[tex]x+y\le20[/tex]We will check if you can catch 11 trout and 9 bass
So, x = 11 and y = 9
So, 11 < 15
and 9 < 10
And (11+9) = 20
so, the answer of the question will be Yes
Because 11 trout and 9 basses are achieving the previous inequalitues.
y=X²-4x-5Domain-Range=Function=
In this problem we have a quadratic equation
y=X²-4x-5
The domain of a quadratic equation is all real numbers
To find out the range we need to calculate the vertex of the parabola
Convert the quadratic equation into vertex form
so
(y-k)=(x-h)^2
y=X²-4x-5
y+5=x^2-4x
complete the square
y+5=(x^2-4x+4)-4
y+5+4=(x-2)^2
y+9=(x-2)^2
the vertex is the point (2,--9)
The quadratic equation represent a vertical parabola open upwards
so the range is the interval
{-9, infinite)
y-1=(x-2)^2 -------> is written as vertex form
The vertex of the parabola is the point (h,k)
(y-k)=(x-h)^2
using a graphing tool to better understand the problem
The range is the interval {-9, infinite)
The domain is the interva (-infinite, infinite)
the function is
y+9=(x-2)^2
f(x)=(x-2)^2-9
or
f(x)=x^2-4x-5
of every five hot dogs Martha sold, 3 had sauerkrauts. what percent of the hot dogs sold had sauerkrauts?a. 6%b. 3/5%c. 60%d. 0.6%
In a survey of 200 people, 32% had a son, 30% had a daughter, and 11% had both a sonand a daughter. What is the conditional probability that a person who has a son also hasa daughter? Round to the nearest whole number.
We have the following probabilites:
[tex]\begin{gathered} P(\text{had a son)=P(s)}=0.32 \\ P(\text{had a daughter)}=P(d)=0.3 \\ P(\text{had both son and daughter)}=P(d\cap s)=0.11 \end{gathered}[/tex]Following the definition of conditional probability:
[tex]P(A|B)=\frac{P(A\cap B)}{P(A)}[/tex]In this case, we want to calculate the conditional probability that a person has a daughter given that he/she already has a son. Then, the probability is:
[tex]P(d|s)=\frac{P(d\cap s)}{P(s)})=\frac{0.11}{0.32}=0.34[/tex]therefore, the conditional probability that a person who has a son also has a daughter is 34%
The Pythagorean theorem Find each missing length to the nearest length
To find any missing length in a right triangle, we use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]Where a is the length of the hypotenuse, the longest side.
In the given right triangle:
• a=8.9
,• b=4
,• c=8
We check if this satisfies the Pythagorean Theorem:
[tex]\begin{gathered} a^2=4^2+8^2 \\ a^2=16+64 \\ a^2=80 \\ a=\sqrt[]{80} \\ a=8.9\text{ units} \end{gathered}[/tex]Thus, we see that the Pythagorean Theorem holds.
sitting with her and not a certain number is a solution to a given inequality
Answer
Check Explanation
Explanation
12) x ≥ -6; 4
This says that x is equal to or greater than -6. So, 4 is greater than -6 and definitely fits this condition. 4 is a solution to the given inequality.
13) n < 8; 11
This says n is less than 8. So, 11 isn't less than 8 and it doesn't fit this condition. 11 is not a solution to this given inequality.
14) k ≤ 2; (4/3)
This says k is less than or equal to 2. So, (4/3) is less than 4 and it fits this condition. (4/3) is a solution to this given inequality.
15) a > 15; 15
This says a is greater than 15. 15 is not greater than 15 and doesn't fit this condition. 15 is not a solution of this inequality.
16) w ≤ -1.6; 1.7
This says w is less than or equal to -1.6. And 1.7 is not less than -1.6 and doesn't fit this condition. 1.7 is not a solution of this inequality.
17) r ≥ (-5/9); (-3/2)
This says r is greater than or equal to (-5/9). And (-3/2) is less than (-5/9) and doesn't fit into this condition. (-3/2) is not a solution of this inequality.
Hope this Helps!!!
Bella has a bucket of Legos. She chose a Lego,recorded the color, and placed it back in the bucket.She did this 40 times. The table shows the results.ColorNumberRed4White10Blue8Green18Based on the results in the table, what is theexperimental probability that the next time Bellachooses a Lego it will be a white or blue?
Answer
Probability that the next time Bella chooses a Lego, it will be a white or blue
= (9/20)
= 0.45
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
Number of white or blue legos = 10 + 8 = 18
Total number of legos = 4 + 10 + 8 + 18 = 40
Probability that the next time Bella chooses a Lego, it will be a white or blue
= (18/40)
= (9/20)
= 0.45
Hope this Helps!!!
A car speeding around a track left skid marks in the shape of an arc of a circle. Thechord distance between the endpoints of the skid marks is 550 feet. The chord is 100feet from the center of the circle.What is the radius of the arc made by the skid marks? Round to the nearest tenth.559.9 ft.256.2 ft.550 ft.540.8 ft.x ft.100 ft292.6 ft.
In the given problem, the chord of the circle forms right triangles with a perpendicular line that passes through the center of the circle. Therefore, the length of the chord is bisected and we get the following triangles:
We can use the Pythagorean theorem to determine the value of the radius:
[tex]r^2=(\frac{550}{2})^2+100^2[/tex]Solving the operations:
[tex]\begin{gathered} r^2=275^2+100^2 \\ r^2=75625+10000 \\ r^2=85625 \end{gathered}[/tex]Now we take the square root to both sides:
[tex]\begin{gathered} r=\sqrt[]{85625} \\ r=292.6 \end{gathered}[/tex]Therefore, the radius of the arc is 292.6 ft.
Jewels homework Culver's multiplication with powers of 10 the first questions of her homework is 32.4 * 10
You invested 17,000 into accounts paying 2%and 8% annual interest respectfully if the total interest earned for the year was 1,060 how much was was invested at each rate2%8%
Let's define the following variables.
x = the amount invested at 2%
y = the amount invested at 8%
0.02x = interest at 2% account
0.08y = interest at 8% account
If the total investment in both accounts is 17, 000 then, we can say that:
[tex]x+y=17,000[/tex]If the total interest earning in both accounts is 1,060 then, we can say that:
[tex]0.02x+0.08y=1,060[/tex]Now that we were able to form a system of equation, we can solve for the values of x and y using substitution method. Here are the steps.
1. Equation Equation 1 into y = .
[tex]\begin{gathered} x+y=17,000 \\ y=17,000-x \end{gathered}[/tex]2. Replace the value of y in equation 2 using equation 1.
[tex]\begin{gathered} 0.02x+0.08y=1,060 \\ 0.02x+0.08(17,000-x)=1,060 \end{gathered}[/tex]3. Solve for x.
[tex]\begin{gathered} \text{Distribute 0.08.} \\ 0.02x+1,360-0.08x=1,060 \\ Subtract\text{ 0.02x and 0.08x.} \\ -0.06x+1,360=1,060 \\ \text{Subtract 1,360 on both sides of the equation.} \\ -0.06x=-300 \\ \text{Divide both sides by -0.06.} \\ x=5,000 \end{gathered}[/tex]The value of x is 5,000. Hence, the amount invested at 2% is 5,000.
4. Solve for y using equation 1 and the calculated value of x.
[tex]\begin{gathered} y=17,000-x \\ y=17,000-5,000 \\ y=12,000 \end{gathered}[/tex]The value of y is 12,000. Hence, the amount invested at 8% is 12, 000.
What is the equation of the line that is parallel to thegiven line and has an x-intercept of -3?
Answer:
[tex]\sf y = \dfrac{-3}{4}x-\dfrac{9}{4}[/tex]
Step-by-step explanation:
Equation of line: y = mx + bHere m is the slope and b is the y-intercept.
First, let us find the slope of given line.
(-4 ,4) & (4 , -2)
[tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-2-4}{4-[-4]}\\\\\\=\dfrac{-6}{4+4}\\\\\\=\dfrac{-6}{8}\\\\\\=\dfrac{-3}{4}[/tex]
Parallel lines have same slope.
m = -3/4
Equation of the line:
[tex]\sf y =\dfrac{-3}{4}x+b[/tex]
At x_intercept, y is 0. (-3 , 0). The line passes through the point (-3 ,0).
Substitute in the above equation and we can find the value of 'b'.
[tex]\sf 0 = \dfrac{-3}{4}*(-3)+b\\\\\\0 = \dfrac{9}{4}+b\\\\\\b = \dfrac{-9}{4}[/tex]
Equation of the required line:
[tex]\sf y =\dfrac{-3}{4}x-\dfrac{9}{4}[/tex]
marla earns an annual salary of $28,000 at her new job. She received a 3% salary increase every year. Find Marla’s total earnings over the course of her first five years working at her job.
ANSWER:
$148,655.8
STEP-BY-STEP EXPLANATION:
Given:
Original salary = $28,000
Increase per year = 3%
The sum of all the earnings would be the sum of the original salary, the salary after 1 year, the salary after 2 years, the salary after 3 years and the salary after 4 years.
The salary in each year is calculated by multiplying the original salary by the increase raised after n years, just like this:
[tex]\begin{gathered} s_n=28000\cdot(1+3\%)^n_{} \\ s_n=28000\cdot(1+0.03)^n_{} \\ s_n=28000\cdot(1.03)^n_{} \end{gathered}[/tex]Therefore, the total earnings would be as follows:
[tex]\begin{gathered} t=28000+28000\cdot(1.03)^1+28000\cdot(1.03)^2+28000\cdot(1.03)^3+28000\cdot(1.03)^4 \\ t=28000+28840+29705.2+30596.4+31514.2 \\ t=148655.8 \end{gathered}[/tex]Therefore, the earnings in the first 5 years of MARla is $148,655.8
S=“
T=“
U=“
V= “
Someone please help
Solve this system of equations by graphing. First graph the equations, and then type the solution.y=3x–1y=–3x–7
In general, to graph a line on the plane, find two points on it and cross them using a straight line.
Finding two points of each of the two lines
[tex]\begin{gathered} y=3x-1 \\ x=1\Rightarrow y=2 \\ \Rightarrow(1,2) \\ x=0\Rightarrow y=-1 \\ \Rightarrow(0,-1) \end{gathered}[/tex]And
[tex]\begin{gathered} y=-3x-7 \\ x=0\Rightarrow y=-7 \\ \Rightarrow(0,-7) \\ x=1\Rightarrow y=-10 \\ \Rightarrow(1,-10) \end{gathered}[/tex]Thus, the graphs are
y=3x-1
y=-3x-7
Graph both lines at the same time, the intersection point is the solution to the system
Thus, the solution is (x,y)=(-1,-4)
[tex]4^-8[/tex] fraction form.
[tex]4^{-8} \\=\frac{1}{4^{8} } \\=\frac{1}{65536}[/tex]
the negative exponent downsize the whole power. That is why as a results we have the fraction.
14. Find the value of x, given that 4(3x + 2) = 44.
Answer:
x = 3
Step-by-step explanation:
Let us use BODMAS:
1) 4(3x + 2) = 44 → We have to multiply 4 by what's in the brackets
2) 12x + 8 = 44 → We have to isolate the 12x, therefore, we have to move 8 to the other side. And remember, when we move a positive number to the other side, it turns negative.
3) 12x = 44 - 8 → Subtract 8 from 44
4) 12x = 36 → Now, we need the x alone. Therefore, we divide 12 by both sides.
5) x = 3
Given that 4(3x+2) = 44 and that 12x+8 = 44, determine the value of x.
12x = 44 - 8
By applying the equation 12x = 36x = 36/12, we can deduce that x = 3.
find the derivative of f(x) = ln √x + √In x
Answer:
[tex]f(x)=in (\sqrt{x} )+\sqrt{in}(x)\\f'(x)=\frac{d}{dx} (in(\sqrt{x} +\sqrt{in}(x)\\\\\\f'(x)=\frac{d}{dx} (in(\sqrt{x} ))+\frac{d}{dx}(\sqrt{in}(x)\\\\ f'(x)=\frac{1}{\sqrt{x} }*\frac{1}{\sqrt[2]{x} } +\frac{1}{\sqrt[2]{in}(x)*\frac{1}{x} } \\\\ f'(x)=\frac{\sqrt{in}(x)+1 }{\sqrt[2x]{in}(x) }[/tex]1:use the differentiation rules
2:find the derivative
3:simplfy
4:solution
I need help on this fast
Find θ to four significant digits for 0< θ<2 π if tan θ= -0.3573
Given:
[tex]tan\theta=-0.3573[/tex]Aim:
[tex]We\text{ need to find the value of }\theta.[/tex]Explanation:
[tex]tan\theta=-0.3573[/tex]Taking inverse trigonometry on both sides.
[tex]tan^{-1}tan\theta=tan^{-1}(-0.3573)[/tex][tex]\theta=tan^{-1}(-0.3573)[/tex][tex]\theta=-19.6618087737[/tex][tex]\theta\approx-19.6618[/tex]We know that
[tex]tan(180+\theta)=tan\theta[/tex][tex]tan(180-19.6618)=tan(-19.6618)[/tex][tex]tan(160.3382)=tan(-19.6618)[/tex]The angels are
[tex]-19.6618\text{ and 160.3382}[/tex]Final answer:
[tex]\theta=19.6618,160.3382[/tex]A shop has 500 items, out of which 5 are defective. What per cent are defective?
Answer:
1%
Step-by-step explanation:
Divide the defective amount by the number of items and multiply into 100, to get the percentage as follows:
5/500 × 100 = 1%
Answer this question and show me how to check it
In order to rewrite these values in the standard form, let's calculate the product with the power of 10 from each number.
For the length, we have:
[tex]\begin{gathered} 8\cdot10^4 \\ =8\cdot10000 \\ =80000\text{ meters} \end{gathered}[/tex]For the thickness, we have:
[tex]\begin{gathered} 5\cdot10^{-6} \\ =5\cdot0.000001 \\ =0.000005\text{ meters} \end{gathered}[/tex]Is the point (20 13) on this line? Explain your reasoning.
In order to determine if the point (20,13) is on the line, it is necessary to write the equation of the line.
The general form of a linear equation is:
y = mx + b
where b is the y-intercept and m is the slope. Y-intercept is the value of y when x = 0. You can observe in the graph that b = 3.
The slope m is conputed by using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are two points of the line. Use the points (0,3) and (6,6), you can select any other two points. Replace these values into the formula for m:
[tex]m=\frac{6-3}{6-0}=\frac{3}{6}=\frac{1}{2}[/tex]Then, the equation of the line is:
[tex]y=\frac{1}{2}x+3[/tex]Now, replace the value of x = 20 in the previous equation, if y = 13, then the point (20,13) in on the line:
[tex]\begin{gathered} y=\frac{1}{2}(20)+3 \\ y=10+3 \\ y=13 \end{gathered}[/tex]Hence, the point (20,13) is on the line