Let x = small drinks
Let y = large drinks
3 small drinks and 2 large drinks contain 108 ounces of cola, this is:
3x + 2y = 108
A small drink contains a third as much cola as a large drink, this is:
x = 1/3y
Then, we solve the system of equations:
[tex]\begin{gathered} 3x+2y=108 \\ x=\frac{1}{3}y \end{gathered}[/tex]First, substitute x in equation 1:
[tex]3(\frac{1}{3}y)+2y=108[/tex]And solve for y:
[tex]\begin{gathered} y+2y=108 \\ 3y=108 \\ \frac{3y}{3}=\frac{108}{3} \\ y=36 \end{gathered}[/tex]Next, substitute y = 36 in x:
[tex]x=\frac{1}{3}y=\frac{1}{3}(36)=12[/tex]Answer:
Small drinks: 12 ounces of cola
Large drinks: 36 ounces of cola
Z (7x+3)° m n (6x+11)
In this problem, the two angles are equal because of the properties, so:
[tex](7x+3)=(6x+11)[/tex]and we can solve for x
[tex]\begin{gathered} 7x-6x=11-3 \\ x=8 \end{gathered}[/tex]So the angles are:
[tex]\begin{gathered} 7(8)+3=59 \\ 6(8)+11=59 \end{gathered}[/tex]Find the angle between the vectors u = 5i – 2j and v = 2i + 3j.
STEP - BY - STEP EXPLANATION
What to find?
The angle between the given vectors.
Given:
u = 5i – 2j and v = 2i + 3j.
To solve the given problem, we will follow the steps below:
Step 1
Write the formula that can be use to solve the above.
[tex]cos\theta=\frac{\vec{a}\vec{.b}}{\vec{|a}\vec{||b}|}[/tex]Step 2
Determine;
→ →
a. b
[tex]\begin{gathered} \vec{a}\vec{.b}=(5)(2)+(-2)(3) \\ \\ =10-6 \\ \\ =4 \end{gathered}[/tex]Step 3
Determine;
→ →
|a| and | b|
[tex]\begin{gathered} \vec{|a|}=\sqrt{5^2+(-2)^2} \\ \\ =\sqrt{25+4} \end{gathered}[/tex][tex]=\sqrt{29}[/tex][tex]\begin{gathered} \vec{|b|}=\sqrt{2^2+3^2} \\ \\ =\sqrt{4+9} \\ \\ =\sqrt{13} \end{gathered}[/tex]Step 4
Substitute the values into the formula.
[tex]\begin{gathered} cos\theta=\frac{4}{\sqrt{29}\times\sqrt{13}} \\ \\ =\frac{4}{\sqrt{377}} \end{gathered}[/tex]Step 5
Take the arc cos of both-side.
[tex]\theta=cos^{-1}(0.20601)[/tex][tex]\theta=78.1\degree[/tex]ANSWER
θ = 78. 1°
iley invested $1,000 in savings bonds. If bonds earn 6.75% interest compounded semi-annually, how much will riley earn in 15 years?
Answer: Riley will earn 2707 in 15 years
Explanation:
The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
where
A is the final amount after t years
A is the principal or initial amount
r is the interest rate
n is the number of compounding periods in a year
t is the time
From the information given,
P = 1000
r = 6.75% = 6.75/100 = 0.0675
t = 15
n = 2 because it was compounded twice in a year
By substituting these values into the formula,
A = 1000(1 + 0.0675/2)^2 * 15
A = 1000(1.03375)^30
A = 2707
Riley will earn 2707 in 15 years
Hello! I need some help with this homework question, please? I just need help with C or D Q2
C) Considering that f(x)=x² we can write the composite function f(f(x)) y plugging into the x-variable the function f(x) itself:
[tex]\begin{gathered} f(f(x)) \\ f\mleft(x\mright)=x^2 \\ f(f(x))=(x^2)^2 \\ f(f(x))=x^4 \end{gathered}[/tex]Now, let's find the Domain. Considering that this is a polynomial function that has no restraints nor discontinuity we can write out the following:
[tex]\begin{gathered} The\: domain\: of\: f\circ f\: is\: all\: Real\: numbers \\ D=\: \mleft(-\infty\: ,\: \infty\: \mright) \end{gathered}[/tex]assume that y varies inversely with x. If y = -4 when x = 1/2 , find x when y=2
it is given that x and y have inverse relation
so K = xy
put y = -4 and x = 1/2
[tex]\begin{gathered} k=\frac{1}{2}\times-4 \\ k=-2 \end{gathered}[/tex]now
y = 2
then'
[tex]\begin{gathered} -2=x\times2 \\ x=\frac{-2}{2} \\ x=-1 \end{gathered}[/tex]so the value of x = -1
[tex]\begin{gathered} x\infty\frac{1}{y} \\ x=\frac{K}{y} \\ K=xy \end{gathered}[/tex]The water level of a tank every minute since it began filling is indicated by segments A,B,and C on the graph
SOLUTION
From the graph
The slope of line A is
[tex]m=\frac{60-20}{2-0}=20[/tex]The slope of line B is
[tex]n=\frac{80-60}{6-2}=5[/tex]The slope of line C is
[tex]p=\frac{110-80}{9-6}=10[/tex]The least segment is the segment with the least slope.
The required arrangement is
[tex]B,C,A[/tex]4Complete the table of values for the following function: y = VX-8X1006493625y-81
y= √x - 8
Replace each value of x and solve for y
x= 100
y= √100 - 8 = 10-8 = 2
x= 64
y= √64-8 = 8 - 8 = 0
x= 9
y= √9 - 8 = 3 - 8 = -5
x= 36
y=√36 - 8 = 6-8= -2
x= 25
y= √25- 8 = 5 - 8 = -3
For the last values, replace y and solve for x
y=-8
-8= √x - 8
-8+8 = √x
0= √x
x= 0^2
x=0
y=1
1=√x-8
1+8= √x
9 = √x
9^2 = x
x= 81
. A town committee has a budget of $75 to spend on snacks for the volunteers participating in aclean-up day. The committeechairperson decides to purchase granola bars and at least 50 bottlesof water. Granola bars cost $.50 each, and bottles of water cost $.75 each. Write and graph asystem of linear inequalities for the number of bottles of water and the number of granola bars thatcan be purchased
Assume that the number of granola bars is x and the number of bottles is y
Since they decided to purchase at least 50 bottles
At least means greater than or equal, so
[tex]x\ge50[/tex]Since the cost of 1 bar = $0.50, then
The cost of all bars = 0.50x
Since the cost of 1 bottle = $0.75, then
The cost of all bottles = 0.75y
Since their budget is $75
They can not exceed that, then
[tex]0.50x+0.75y\le75[/tex]The solution will be in the common part of the two colors
The red represents the second inequality
The blue represents the first inequality
what is the slope of the equation y = - 7x + 9
EXPLANATION
The slope of a line is given by the following expression:
[tex]\text{Slope = }\frac{rise}{run}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]In this case, we have that the slope is represented by the generic form:
y = mx + b
Where m is the slope and b is the y-intercept.
So, the slope is -7.
Answer: m=-7
Use the change of base formula to compute log/174.Round your answer to the nearest thousandth.
Answer:
The Expression is given below as
[tex]\log_{\frac{1}{7}}4[/tex]Represent the expression above to be
[tex]=x[/tex]That is, we will have that
[tex]\log_{\frac{1}{7}}4=x[/tex]Applying the change of base rule below, we will have that
[tex]\begin{gathered} \log_ab=y \\ b=a^y \\ lnb=lna^y \\ lnb=ylna \\ y=\frac{lnb}{lna} \end{gathered}[/tex][tex]\begin{gathered} \log_{\frac{1}{7}}4=x \\ (\frac{1}{7})^x=4 \\ (7^{-1})^x=4 \\ 7^{-x}=4 \\ take\text{ ln of both sides} \\ ln7^{-x}=ln4 \\ -xln7=ln4 \\ dividie\text{ both sides by -ln7} \\ \frac{-xln7}{-ln7}=\frac{ln4}{-ln7} \\ x=-0.712 \end{gathered}[/tex]Hence,
The final answer is
[tex]\rightarrow-0.712[/tex]A survey claims that the percent of a city's residents that favor building a new football stadium is likely between 52.3% and 61.7%. What was the sample proportion (what percent of the people in the sample survey said that they wanted to build a new stadium )?
The confidence interval for the sample proportion is calculated using the following formula:
[tex]\lbrack p\lbrack\text{hat\rbrack}\pm Z_{1-\frac{\alpha}{2}}\cdot\sqrt[]{\frac{p\lbrack hat\rbrack(1-p\lbrack hat\rbrack)}{n}}\rbrack[/tex]Where p[hat] represents the sample proportion. As you see you add/subtract the margin of error to the sample proportion to determine both bonds of the interval, which means that the sample proportion is in the middle of the interval.
The percent of residents in favor of building a new football stadium is between 52.3% and 61.7% → the sample proportion used to determine this interval is in the middle of both bonds. To calculate the said value you have to find the average of both values:
[tex]52.3\%The sample proportion used to estimate the interval was p[hat]=0.57
i only need the final answers, i do not need an explanation i am just double checking my final answer
In quadrilateral BADC, AB = AD andBC = DC. The line AC is a line ofsymmetry for this quadrilateral
Given the quadilateral: BADC
AB = AD
BD = DC
The line AC is a diagonal of the quadilateral.
The given quadilateral is a kite.
Let's answer the following questions using the given information.
Part a:
Diagonal AC and diagonal BD are perpendicular.
The diagonals of a kite are perpendicular, this is because the point of intersection of both diagonals form a right angle (90 degrees).
Therefore, based on the line of symmetry, we can say diagonals AC and BD are perependicular because the quadilateral is symmetric along the diagonals AC and BD of the figure.
• Part b:
Based on the line of symmetry, angle ABC and angle ADC have the same measure because the qudilateral has
Convert the following mixed number to an improper fraction: 28 1 / 8 What is the numerator of this improper fraction? State the answer without reducingAll negatives must be included in your final answer:ie. if the question asks for the whole number portion, numerator, or denominator of the answer and it has a negative, you must include that negative.Be sure to reduce all fractions fully and convert improper fractions to mixed numbers before stating your final answer
Given the mixed number:
[tex]28\frac{1}{8}[/tex]Let's convert the mixed number to an improper fraction.
To convert a mixed number to improper fraction, multiply the denominator by the whole number, then add the result to the numerator.
Thus, we have:
[tex]\begin{gathered} 28\times8=224 \\ \Longrightarrow224+1=225 \end{gathered}[/tex]Therefore, the improer fraction is:
[tex]\frac{225}{8}[/tex]The numerator is the number at the top of the fraction.
Therefore, the numerator of this improper fraction is = 225
ANSWER:
[tex]\frac{225}{8}[/tex]Numerator = 225
Answer: To convert a mixed number to improper fraction multiply the whole number and the denominator and then add the numerator. This gives the numerator of the improper fraction. The denominator is the same as the denominator of the given mixed number.
Step-by-step explanation:
[tex]28\frac{1}{8}[/tex] = [28x8+1] / 8 = [tex]\frac{224+1}{8}[/tex] = [tex]\frac{225}{8}[/tex]
The numerator of [tex]\frac{225}{8}[/tex] is 225
To learn more about conversion of mixed number to improper fraction:
https://brainly.in/question/28231026
Use the Venn diagram to complete the sentences. Write All or Some or No in each blank
If we look at the image, we must see that the parallelogram's circle is greater than the trapezoid's circle, in other words, the trapezoids are contained in the parallelograms. In addition, no information about the quadrilaterals is provided in the Venn diagram. The correct word in each sentence are
1. No trapezoids are quadrilaterals.
2. No quadrilaterals are trapezoids.
3. Some parallelograms are trapezoids.
4. All trapezoid are parallelograms.
Which equation models the total profit,y,based on the number of tickets sold,x?
Answer
D. y - 300 = 4(x - 100)
Step-by-step explanation
Variables
• x: tickets sold
,• y: profit
Equation of a line in point-slope form
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x₁, y₁) is a point on the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]This line passes through the points (100, 300), that is, when 100 tickets are sold, the club had $300 in profit, and the point (200, 700). Then, its slope is:
[tex]\begin{gathered} m=\frac{700-300}{200-100} \\ m=\frac{400}{100} \\ m=4 \end{gathered}[/tex]Substituting into the general equation with m = 4 and the point (100, 300), we get the next equation of the line:
[tex]y-300=4(x-100)[/tex]Drag the prisms to the table in order from least volume to greatest volume.
Fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The volume of first prism with sides 2, 1.5 and 3.2
Volume=2×1.5×3.2
=9.6 in³
The volume of second prism with sides 1.5, 1.5 and 6
Volume=1.5×1.5×6
=13.5 in³
The volume of third prism with sides 2, 5/2 and 7/2
Volume=2×2.5×3.5
=17.5 in³
The volume of fourth prism with sides 1/2, 1/2 and 1/2
Volume=0.5×0.5×0.5
=0.125 in³
Hence fourth prism, first prism, second prism and fourth prism is order from least volume to greatest.
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ1
choose the image that corresponds to Figure 1 after a reflection over the x-axis and a translation of one unit left
Solution
For this case the solution would be given by:
what is the volume of the cone? use Pi and round to the nearest tenth
Let's begin by listing out the information given to us:
Radius (r) = 7ft
Height (h) = 25ft
The volume of a cone is calculated as shown below:
V = ⅓πr²h
V = ⅓ * 3.14 * 7² * 25 = 1282 1/6
V = 1282 1/6 or 1282.667 = 1282.7 = 1283 ft³
V = 1283 ft³
How do I write five hundred and eight hundredths as a decimal number.
start by writing the whole part, sine there us only hundreds we can write it as
[tex]500[/tex]then write the decimal part, we can see that there are no tenths in this expression so we start with a 0, then for the hundredths, we can put the number 8
[tex].08[/tex]The complete number should be
[tex]500.08[/tex]List the coordinates coordinates of vertices of trapezoid ABCD after it has been rotated 90 Counterclockwise bout the origin and then reflected over the x-axis. A(-5,-3) B(-4,0),c(-2,0),D(O,-3)
Answer:
The coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]Explanation:
From the question, the pre-image was been rotated 90 Counterclockwise bout the origin.
Which has a rule;
[tex](x,y)\rightarrow(-y,x)[/tex]Applying the rule to the given points. we have;
[tex]\begin{gathered} A(-5,-3)\rightarrow A^{\prime}(3,-5) \\ B(-4,0)\rightarrow B^{\prime}(0,-4) \\ C(-2,0)\rightarrow C^{\prime}(0,-2) \\ D(0,-3)\rightarrow D^{\prime}(3,0) \end{gathered}[/tex]Then the produced image was then reflected over the x-axis;
Reflection across the x-axis have the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Applying the rule to the resulting image;
[tex]\begin{gathered} A^{\prime}(3,-5)\rightarrow A^{\prime^{}}^{\prime}(3,5) \\ B^{\prime}(0,-4)\rightarrow B^{\prime}^{\prime}(0,4) \\ C^{\prime}(0,-2)\rightarrow C^{\prime^{}}^{\prime}(0,2) \\ D^{\prime}(3,0)\rightarrow D^{\prime}^{\prime}(3,0) \end{gathered}[/tex]Therefore, the coordinates of the final image is;
[tex]A^{\prime\prime}(3,5),B^{\prime\prime}(0,4),C^{\prime}^{\prime}(0,2),D^{\prime}^{\prime}(3,0)[/tex]PLEASE HELP!!!!! I WILL GIVE BRAINLIEST!!!!
Evaluate the expression . Write your answer as a simplified mixed number, or as a decimal. Show your work
Answer:
[tex]-3\frac{15}{16}[/tex]
Step-by-step explanation:
Given:
[tex](-\frac{1}{4}+2.875)\div(-\frac{2}{3})[/tex]
First, convert 2.875 to an improper fraction:
[tex]2.875=2\frac{875}{1000}=2\frac{7}{8}=\frac{23}{8}[/tex]
The expression becomes:
[tex](-\frac{1}{4}+\frac{23}{8})\div(-\frac{2}{3})[/tex]
Then, add the terms in the parentheses:
[tex]-\frac{1}{4}+\frac{23}{8}=-\frac{2}{8}+\frac{23}{8}=\frac{21}{8}[/tex]
The new expression is:
[tex]\frac{21}{8}\div-\frac{2}{3}[/tex]
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. Therefore:
[tex]\frac{21}{8}\times-\frac{3}{2}[/tex]
Next, multiply the numerators and denominators:
[tex]-\frac{63}{16}[/tex]
Finally, simplify to a mixed fraction:
[tex]-3\frac{15}{16}[/tex]
find the area of a hexagon with sides 20 mm long. Round your answer to the nearest tenth
When you know the length of the sides of a hexagon you use the next formula to find its area:
[tex]A=\frac{3\sqrt{3}}{2}s^2[/tex]s is the length of the sides
For the given hexagon:
[tex]\begin{gathered} A=\frac{3\sqrt{3}}{2}(20mm)\placeholder{⬚}^2 \\ \\ A=\frac{3\sqrt{3}}{2}(400mm^2) \\ \\ A=3\sqrt{3}(200mm^2) \\ \\ A=600\sqrt{3}mm^2 \\ \\ A\approx1039.2mm^2 \end{gathered}[/tex]Then, the area of the given hexagon is 1039.2 square millimetersIts a project for my consumer math class and i have to record all the information on a template
We are asked to fill up the transactions in the table.
Remember that Payments, fees, and withdrawals are always subtracted from the balance, and deposits are always added to the balance.
The starting balance is $275
1st transaction:
Payment of $85.67 to the electric company on 2nd October.
Since it is a payment, it must be subtracted from the previous balance.
Balance = $275 - $85.67 = $189.33
2nd transaction:
You want to deposit the $20 that your friend gave to you.
Since it is a deposit, it must be added to the previous balance.
Balance = $189.33+$20 = $209.33
Solve $9.75 x $40 to get $390.00, using long multiplication
I will be using a rough sketcher to show the long multiplication:
The process is shown below:
Note:
the last zero is taken down last, after the multiplication is done [shown by green arrow]
Lastly, we put the decimal point "2 places to the left" since the multiplication problem has "2 decimal places"
12. To prepare an aquarium for use, you can clean it with a saltwater solution. The amount of salt varies directly with the volume of the water. The solution has 2 teaspoons of aquarium salt for every gallon of water. a. How many teaspoons of aquarium salt are needed for 5 gallons of water? b. Write an equation that relates x gallons of water to y teaspoons of salt. c. Use the equation to find the number of gallons of water to use for 12 teaspoons of salt.
Given:
The solution has 2 teaspoons of aquarium salt for every gallon of water.
a.) How many teaspoons of aquarium salt are needed for 5 gallons of water?
- To be able to determine how many teaspoons of aquarium salt are needed, we will be using ratios and proportions.
[tex]\text{ 2 teaspoon of salt : 1 gallon of water = x : 5 gallons of water}[/tex]Where,
x = teaspoons of aquarium salt
We get,
[tex]\text{ 2 teaspoon of salt : 1 gallon of water = x : 5 gallons of water}[/tex][tex]\frac{2}{1}\text{ = }\frac{x}{5}[/tex][tex]\text{ (2)(5) = (x)(1)}[/tex][tex]\text{ 10 = x}[/tex]Therefore, you will be needing 10 teaspoons of aquarium salt for 5 gallons of water.
b.) Write an equation that relates x gallons of water to y teaspoons of salt.
Let,
x = gallons of water
y = teaspoons of salt
[tex]\text{ }\frac{2\text{ teaspoons of salt}}{1\text{ gallon}}\text{ = }\frac{y}{x}\text{ }\rightarrow\text{ }\frac{2}{1}\text{ = }\frac{y}{x}\text{ }\rightarrow\text{ 2 = }\frac{y}{x}[/tex][tex]\text{ 2x = y}[/tex]Therefore, the equation of the mixture will be 2x = y.
c.) Use the equation to find the number of gallons of water to use for 12 teaspoons of salt. Substitute, y = 12.
[tex]\text{ 2x = y}[/tex][tex]\text{ 2x = 12}[/tex][tex]\text{ }\frac{2x}{2}\text{ = }\frac{12}{2}[/tex][tex]\text{ x = 6}[/tex]Therefore, you will be needing 6 gallons of water for 12 teaspoons of salt.
5) A ball is dropped from a height of 400 feet. Each time it hits the ground, it rebounds 75% of the distance it has fallen. How far will the ball travel before coming to rest?
Initial height: 400 m
Each time it hits the ground, it rebounds 75% the distance it has fallen. Let us say this distance is d, then the new height is:
[tex]\begin{gathered} h=75\text{\% of }d=\frac{75}{100}\cdot d \\ \Rightarrow h=\frac{3}{4}d \end{gathered}[/tex]If the initial height is 400 m, then the subsequent heights are given by the recurrence equation:
[tex]\begin{gathered} h_0=400 \\ h_n=(\frac{3}{4})^n\cdot h_0 \\ \Rightarrow h_n=400\cdot(\frac{3}{4})^n \end{gathered}[/tex]And the total distance traveled D is:
[tex]\begin{gathered} D=h_0+2\cdot\sum ^{\infty}_{n\mathop=1}\lbrack(\frac{3}{4})^n\cdot h_0\rbrack \\ \Rightarrow D=400+800\cdot\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n \end{gathered}[/tex]Now, let us analyze the sum term:
[tex]\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=\frac{3}{4}+(\frac{3}{4}_{})^2+(\frac{3}{4})^3+\cdots_{}[/tex]From the infinite geometric sequence:
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop=0}r^n=\frac{1}{1-r} \\ \Rightarrow\sum ^{\infty}_{n\mathop{=}1}r^n=\frac{1}{1-r}-1 \end{gathered}[/tex]Where r < 1. From our problem, r = 3/4 < 1, then:
[tex]\begin{gathered} \sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=\frac{1}{1-\frac{3}{4}}-1=\frac{1}{\frac{1}{4}}-1=4-1 \\ \Rightarrow\sum ^{\infty}_{n\mathop{=}1}(\frac{3}{4})^n=3 \end{gathered}[/tex]Finally, using this result:
[tex]D=400+800\cdot3=400+2400=2800[/tex]What is the x-value of the solution to this system of equations? x = 2y - 4 7x + 5y = -66 F-2 G 19 7 H -8 62 19
Answer:
x = -8
Explanation:
Given the below system of equations;
[tex]\begin{gathered} x=2y-4\ldots\ldots\ldots\ldots\ldots\text{.Equation 1} \\ 7x+5y=-66\ldots\ldots\ldots\ldots\text{Equation 2} \end{gathered}[/tex]The solve the above, let's go ahead and put equation 1 into equation 2 and solve for y;
[tex]\begin{gathered} 7(2y-4)+5y=-66 \\ 14y-28+5y=-66 \\ 19y=-66+28 \\ 19y=-38 \\ y=-\frac{38}{19} \\ y=-2 \end{gathered}[/tex]To find x, we have to substitute the value of y into equation 1 and solve for x;
[tex]\begin{gathered} x=2(-2)-4=-4-4=-8 \\ x=-8 \end{gathered}[/tex]I need help with this problem. Please show work and simplify the answer!
the first three terms of a sequence are given around the nearest thousandth if needed 16,4,1,... Find the 6th term
16, 4, 1....
2^4, 2^2, 2^0
[tex]2^4,2^2,2^0,2^{-2},2^{-4},2^{-6},2^{-8}\ldots[/tex]6th term would be 2^-6:
[tex]2^{-6}[/tex]Series