Let:
• A ,be the number of millilitres (mL) of solution A used.
,• B ,be the number of mL of solution B used.
We know that Dale uses four times as much solution A as solution B, meaning
[tex]A=4B[/tex]Now, we know that we will end up with 570 mL of pure alcohol in the final solution. Using the dilution of both A and B (20% means 0.2 and 15% is 0.15) we would have that:
[tex]0.2A+0.15B=570[/tex]We would have the following system of equations:
[tex]\begin{cases}A=4B \\ 0.2A+0.15B=570\end{cases}[/tex]Substituting equation 1 in equation 2 and solving for B :
[tex]\begin{gathered} 0.2A+0.15B=570 \\ \rightarrow0.2(4B)+0.15B=570 \\ \rightarrow0.8B+0.15B=570 \\ \rightarrow0.95B=570\rightarrow B=\frac{570}{0.95} \\ \Rightarrow B=600 \end{gathered}[/tex]Substituting in equation 1 and solving for A:
[tex]\begin{gathered} A=4B \\ \rightarrow A=4(600) \\ \Rightarrow A=2400 \end{gathered}[/tex]This way, we can conclude that 2400 mL of solution A and 600mL of solution B were used.
I just want to go to sleep but I need the answer to this question
The average rate of change of a function f(x) from x1 to x2 is given by:
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case we need the first three seconds so x1=0 and x2=3.
Calculate the values of the function at x=0 and x=3 to get:
f(0)=150 and f(3)=0.
Substitute these values into the formula for average rate of change:
[tex]\begin{gathered} \frac{f(3)-f(0)}{3-0} \\ =\frac{0-150}{3} \\ =\frac{-150}{3} \\ =-50 \end{gathered}[/tex]Hence the avearage rate of change of the function for the first three seconds is -50.
Note that the negative sign shows that the function is decreasing in the time interval (first three seconds).
Tj earns a 20% commission on all sales plus a base salary of 40k. his total income last year was at least 70k. which inequality can be used to calculate the minimum of Tj sales.
Let x be the all sale for individual.
Determine the expression for total income of individual.
[tex]\frac{20}{100}x+40000=0.2x+40000[/tex]The total income was at least 70000. So last year income is 70000 or more than 70000.
Setermine the inequality for the sales.
[tex]\begin{gathered} 0.2x+40000-40000\ge70000-40000 \\ \frac{0.2x}{0.2}\ge\frac{30000}{0.2} \\ x\ge150000 \end{gathered}[/tex]Americans who are 65 years of age or older make up 13.2% of the total population. If there at 30.3 million american in this age group, find the total u.s. population
Given:
Americans who are 65 years of age or older make up 13.2% of the total population.
Required:
The total u.s. population
Explanation:
Let the total population of u.s be x.
According to the given condition.
[tex]13.2\text{ \% of x = 30.3 billion}[/tex]Therefore,
[tex]\begin{gathered} \frac{13.2}{100}\text{ }\times\text{ x = 30.3} \\ x\text{ = }\frac{30.3\text{ }\times\text{ 100}}{13.2} \\ x\text{ = 229.55 billion} \end{gathered}[/tex]Answer:
Thus the total population of u.s is 229.55 billion.
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
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:h(x) = (x − 1)^2− 9.
The function is
[tex]h(x)=(x-1)^2-9[/tex]1) x-intercept(s)
The x-intercepts refer to the points on which the function intercepts with the x-axis, in other words, when y=h(x)=0
So, given that condition, we get
[tex]\begin{gathered} h(x)=0 \\ \Rightarrow(x-1)^2-9=0 \\ \Rightarrow x^2-2x+1^{}-9=0 \\ \Rightarrow x^2-2x-8=0 \\ \Rightarrow(x-4)(x+2)=0 \end{gathered}[/tex]Therefore, there are two x-intercepts, and those are the points
[tex](4,0),(-2,0)[/tex]2) y-intercepts
The y-intercepts happen when x=0. So,
[tex]\begin{gathered} x=0 \\ \Rightarrow h(0)=(0-1)^2-9=1-9=-8 \end{gathered}[/tex]So, there is only one y-intercept and it's on the point (0,-8)
3) Vertex
The general equation of a parabola is
[tex]y=f(x)=a^{}x^2+bx+c[/tex]There is another way to express the same function, which is called the 'vertex form':
[tex]\begin{gathered} y=f(x)=a(x-h)^2+k \\ \Rightarrow y=ax^2-2ahx+ah^2+k \end{gathered}[/tex]What is particularly useful of this vertex form is that the vertex is the point (h,k)
So, transforming h(x) into vertex form:
[tex]\begin{gathered} h(x)=(x-1)^2-9=a(x-h)^2+k \\ \Rightarrow\begin{cases}a=1 \\ h=1 \\ k=-9\end{cases} \end{gathered}[/tex]Therefore, the vertex is the point (h,k)=(1,-9)
4) Axis of symmetry
In general, the equation of the axis of symmetry is given by
[tex]x=-\frac{b}{2a};y=f(x)=ax^2+bx+c[/tex]Therefore, in our particular problem,
[tex]\begin{gathered} h(x)=x^2-2x-8=ax^2+bx+c \\ \Rightarrow\begin{cases}a=1 \\ b=-2 \\ c=-8\end{cases} \\ \end{gathered}[/tex]Thus, the equation of the line that is the axis of symmetry is
[tex]x=-\frac{b}{2a}=-\frac{(-2)}{2\cdot1}=-\frac{(-2)}{2}=1[/tex]Then, the axis of symmetry is the line x=1.
Summing up the information in the four previous steps, we get
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77. How much was the tip as a percentage of the bill?
Percentage of the bill = 0.185*100=18.5%
ABCD is a rectangle. Find the length of AC and the measures of a and f.
SOLUTION
Consider the diagram
We need to obtain the value of length AC
Using the pythagoras rule, we have
[tex]undefined[/tex]
9Which is the best name for a quadrilateral with vertices at A(5,-2), B(2,2), C(1,-5), and D(-2,-1)?A parallelogramB squarerhombusD rectangle
Parallelogram. Option A is correct
Explanations:In order to determine the best name for a quadrilateral with the given vertices, we will find the measure of the distance AB, BC, CD, and AD using the distance formula as shown;
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y^{}_1)^2}[/tex]For the measure of AB with coordinates A(5,-2), B(2,2);
[tex]\begin{gathered} AB=\sqrt[]{(5-2)^2+(-2-2^{}_{})^2} \\ AB=\sqrt[]{3^2+(-4)^2} \\ AB=\sqrt[]{9+16} \\ AB=\sqrt[]{25} \\ AB=5 \end{gathered}[/tex]For the measure of BC with coordinates B(2,2) and C(1, -5)
[tex]\begin{gathered} BC=\sqrt[]{(2-1)^2+(2-(-5^{}_{}))^2} \\ BC=\sqrt[]{1^2+7^2} \\ BC=\sqrt[]{50} \\ BC=5\sqrt[]{2} \end{gathered}[/tex]For the measure of CD with coordinates C(1,-5), and D(-2,-1);
[tex]\begin{gathered} CD=\sqrt[]{(1-(-2))^2+(-5-(-1^{}_{}))^2} \\ CD=\sqrt[]{3^2+(-4)^2} \\ CD=\sqrt[]{9+16} \\ CD=\sqrt[]{25} \\ CD=5 \end{gathered}[/tex]For the measure of AD with coordinates A(5, -2), and D(-2,-1);
[tex]\begin{gathered} AD=\sqrt[]{(5-(-2))^2+(-2-(-1^{}_{}))^2} \\ AD=\sqrt[]{(5+2)^2+(-2+1)^2} \\ AD=\sqrt[]{7^2+(-1)^2} \\ AD=\sqrt[]{50} \\ AD=5\sqrt[]{2} \end{gathered}[/tex]For the slopes;
Check if the length AB is perpendicular to AD
[tex]\begin{gathered} m_{AB}=\frac{2+2}{2-5} \\ m_{AB}=-\frac{4}{3} \end{gathered}[/tex]For the slope of AD
[tex]\begin{gathered} m_{AD}=\frac{-1+2}{-2-5} \\ m_{AD}=-\frac{1}{7} \end{gathered}[/tex]Since AB is not perpendicular to AD, hence the quadrilateral is not a rectangle and also not a square or rhombus since all the sides are not equal.
From the given distances, you can see that opposite sides are equal (AB = CD and BC = AD ), hence the best name for a quadrilateral is a parallelogram.
Which cosine function has maximum of 2, a minimum of –2, and a period of 2pi/3 ?
Given:
maximum = 2, minimum = -2
period = 2π/3
Find: the cosine function having those attributes stated above
Solution:
Cosine equations follow the pattern below:
[tex]y=Acos(B(x-C))+D[/tex]where A = amplitude, B = 2π/period, C = horizontal shift, and D = vertical shift.
Since the only given information is the period, let's calculate for the value of B.
[tex]B=\frac{2\pi}{period}\Rightarrow B=\frac{2\pi}{\frac{2\pi}{3}}=3[/tex]Out of the choices, only y = 2cos 3θ has the value of B which is 3. Hence, y = 2cos 3θ is the cosine function that has a maximum of 2, a minimum of –2, and a period of 2pi/3. (Option 3)
You are offered two different furniture sales jobs. The Furniture Barn offers you a job that pays straight commission of 6% of the sales. The Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. How much would you have to sell in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse? Round the answer to the nearest cent.
The Furniture Barn pays the same as The Furniture Warehouse if my sales are $
The amount to be sold in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse is $7000.
How to calculate the value?Lat the amount of sales be represented as x.
Since the Furniture Barn offers you a job that pays straight commission of 6% of the sales. This will be:
= 6% × x = 0.06x
Also, the Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. This will be:
= 350 + (1% × x)
= 350 + 0.01x
The equation will be expressed as:
0.06x = 350 + 0.01x
Collect like terms
0.06x - 0.01x = 350
0.05x = 350
Divide
x = 350 / 0.05
x = 7000
The sale is $7000.
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what is the slope formula of (4,2) and (7, 6.5)
Suppose the given coordinates are represented as,
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ (x_2,y_2)=(7,6.5) \end{gathered}[/tex]Then, the formula for slope can be expressed as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6.5-2}{7-4} \end{gathered}[/tex]Solving it,
[tex]m=\frac{4.5}{3}=1.5[/tex]The slope is 1.5.
The formula of (10, 8) anjd (-5,8) is
[tex]m=\frac{8-8}{-5-10}[/tex]AABC - ADEF? Explain your reasoning. E 6 units C 40° 9 units 4 units 6 units er your answer and explanation.
Side-Angle-Side Theorem states that triangles are congruent if any pair of corresponding sides and their included angle are congruent.
How do we know that their sides are congruent, by similarity ratios, means a ratio of the lengths of the sides to see if they have the same ratio or scale factor:
[tex]\begin{gathered} \frac{9}{6}=1.5 \\ \frac{6}{4}=1.5 \end{gathered}[/tex]Then, since their sides are congruent and they have the same angle, they are congruent by SAS.
OA.y> -22² +10z - 8OB. y<-2x² +102-8OC. y2-22² +10r - 8OD. y ≤-22² +10z - 8
Solution:
Using a graph plotter,
The correct answer that satisfies the graph is OPTION C.
Calculate the determinant of this 2x2 matrix. Provide the numerical answer. |2 -1 | |4 -5|
Given the matrix
[tex]\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}{}\end{bmatrix}[/tex]its determinant is computed as follows:
ad - cb
In this case, the matrix is
[tex]\begin{bmatrix}{2} & {-1} & \\ {4} & -5 & {}\end{bmatrix}[/tex]and its determinant is
2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6
Convert 6 kg per inch to g per m 6 points
We can do this conversion in this way:
[tex]\frac{6\operatorname{kg}}{i}\cdot\frac{1000gr}{\operatorname{kg}}\cdot\frac{1i}{0.0254m}=23622.047g/m[/tex]Then, the answer is 23622.047g/m.
triangle OPQ is similar to triangle RST. Find the measure of side RS. Round your answer to the nearest tent if necessary
To answer this question, we have that, if two triangles are similar, they maintain the same proportion on their corresponding sides.
We have that the corresponding sides are QP and TS, OP and RS, and QO and TR, so we can write:
[tex]\frac{TS}{QP}=\frac{RS}{OP}=\frac{TR}{QO}[/tex]Then, since we have the values for QP, TS, and OP, we can find RS using the above proportion:
[tex]\frac{TS}{QP}=\frac{RS}{OP}\Rightarrow\frac{41.4}{11}=\frac{RS}{8}\Rightarrow RS=\frac{41.4\cdot8}{11}=\frac{331.2}{11}\Rightarrow RS=30.109090\ldots[/tex]Then, we have that we can round this value to 30.11 units, and if we round the answer to the nearest tenth, we finally have that RS = 30.1 units.
Answer:
x = 30.1 (round 30)
Step-by-step explanation:
being similar we can solve with a simple equation
11 : 8 = 41.4 : x
x = 8 × 41.4 : 11
x = 331,2 : 11
x = 30.1 (round 30)
Create a polynomial of degree 6 that has no real roots. Explain why it has no real roots.
Answer:
Explanation:
We're asked to create a polynomial of degree 6 that has no real roots.
Let's consider the below polynomial;
[tex]x^6+1=0[/tex]To determine its roots, we'll follow the below steps;
Step 1: Subtract 1 from both sides of the equation;
[tex]undefined[/tex]circumference of the back wheel=9 feet, front wheel=7 feet. On a certain distance the front wheel gets 10 revolutions more than the back wheel. What is the distance?
The distance would be 315 feet which is a certain distance the front wheel gets 10 revolutions more than the back wheel.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given that the circumference of the back wheel=9 feet, the front wheel=7 feet. At a certain distance, the front wheel gets 10 revolutions more than the back wheel.
Both wheels must move at the same distance. If the number of revolutions taken by the back wheel is x, then the number of revolutions taken by the front wheel is x+10.
Because the distance traveled is the same as:
⇒ 9x = 7(x+10)
⇒ 9x = 7x+70
⇒ 9x - 7x = 70
⇒ 2x = 70
⇒ x = 35
We obtain x = 35 revolutions.
So the total distance traveled is 35×9=315 feet or 45×7=315 feet.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.(14+3)(2 x 6)B▸ Math symbols▸ Relations▸ Geometry▸ Groups▸ TrigonometryStatistics▸ Greek
Given:
The given mathematical expression is,
[tex](14+3)-(2\times6)[/tex]Required:
To solve the given expression.
Explanation:
Let us solve the given mathematical expression by using BODMAS rule.
Therefore, first, we calculate within brackets and then will perform subtraction.Thus, we get,
[tex]\begin{gathered} (14+3)-(2\times6) \\ =17-12 \\ =5 \end{gathered}[/tex]Final Answer:
The solution of the given mathematical expression is, 5.
Translate the following word phrases to an algebraic expression and simplify: “8 times the difference of 6 times a number and 3”
SOLUTION:
Step 1:
In this question, we are meant to:
Translate the following word phrases to an algebraic expression and simplify:
“8 times the difference of 6 times a number and 3”
Step 2:
Assuming the unknown number be y, we have that:
[tex]\begin{gathered} 8\text{ ( 6y - 3 )} \\ =\text{ 48 y - 24} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]48y\text{ - 24}[/tex]
Find the area of the yellow region. Round to the nearest tenth. 7.53cm
The figure shows a square inscribed in a circle of radius r = 7.53 cm.
The yellow region corresponds to the area of the circle minus the area of the square.
The area of a circle of radius r is:
[tex]A_c=\pi r^2[/tex]Calculating:
[tex]A_c=\pi(7.53\text{ cm})^2=178.13\text{ }cm^2[/tex]The radius of the circle is half the diagonal of the square. The diagonal of the square is:
d = 2 x 7.53 cm = 15.06 cm
The area of a square, given the diagonal d, is calculated as follows:
[tex]A_s=\frac{d^2}{2}[/tex]Calculating:
[tex]\begin{gathered} A_s=\frac{(15.06\text{ cm})^2}{2} \\ \\ A_s=113.40\text{ }cm^2 \end{gathered}[/tex]The required area is:
A = 178.13 - 113.40 = 64.73 square cm
Find d the side length of a square given the area of the square
Area of a square = side length ^2
Given: A= 20.25
Replacing:
20.25 = s^2
√20.25 = s
s = 4.5 m
Martin finds an apartment to rent for $420 per month. He must pay a security deposit equal to one and a half months' rent. How much is the security deposit? Alexis earns $31,350 per year. According to the banker's rule, how much money can she afford to borrow for a house?
if one month is $420
and the security deposit is one and a half month= 1.5*$420
1.5*420=630
So the answer is: 630
passes through (1,3) and parallel to y=-x
The equation of a line parallel to y=-x and passes through (1,3) is x+y=4
What is the relationship between coordinates and the equation of a line?The coordinates of a line pass through the equation of a line.
What is the relationship between two parallel lines?Two parallel lines make the same angle with respect to the x-axis ie. make the same slope.
We have been given that the line is parallel to y=-x or x+y=0
Thus, they will be having the same slope which is -1.
Since, in the equation Ax+By+C=0, the slope is equal to -A/B
So putting the values in the equation y=mx+c where m is the slope and c is the constant
y=-x+c
Now we know that the equation passes through (1,3)
So, putting values 1=-3+c which gives c=4
Therefore, the equation of the line is y=-x+4 or x+y=4.
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what is the substitution for f7=3(x)^2+2(x)-9
Given a function f(x), whenever you want to evaluate the function, you simply change the variable for the value you where you want to evaluate the function at, and then perform the mathematical operations the function tells you to do.
In our case f(x) = 3x^2 + 2x -9
If we evaluate f(x) at x=7, then
[tex]f(7)=3(7)^2+2(7)\text{ -9 = 3 }\cdot\text{ 49 + 2}\cdot\text{ 7 - 9 = 152}[/tex]So f(7) = 152.
Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16 or 4
Step-by-step explanation:
-6-10=-16
10-6=4
Question : Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16
{x|x ≤ - 6}
Write written interval motion and graph the interval
The inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
What exactly is interval notation?
The number line's left to right location in the solution is indicated using interval notation (i.e., which part of the number line is shaded). Endpoints that are part of the solution are denoted by parentheses, while those that are not are denoted by brackets.For instance, the expressions -3x2, [-3,2], and xR|-3x2 denote that x is between -3 and 2 and might be either endpoint.Interval Notation x<-6. x<−6 x < - 6.
Convert the inequality to interval notation. (−∞,−6) ( - ∞ , - 6 ).
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Hey need your help it’s the one about the %
Answer:
[tex]\text{\$}$219.27$[/tex]Explanation:
We were given that:
Pamela bought an electric drill at 85% off the original price (she bought it at 15% of the original price)
She paid $32.89 for the drill
The regular price is calculated using simple proportion as shown below:
[tex]\begin{gathered} 15\text{\%}=\text{\$}32.89 \\ 100\text{\%}=\text{\$}x \\ \text{Cross multiply, we have:} \\ x\cdot15\text{\%}=\text{\$}32.89\cdot100\text{\%} \\ x=\frac{\text{\$}32.89\cdot100\text{\%}}{15\text{\%}} \\ x=\text{\$}219.27 \\ \\ \therefore x=\text{\$}219.27 \end{gathered}[/tex]Therefore, the regular price was $219.27
Sally deposits $2,500 at 8% interest for 3 years . How much can she withdraw at the end of that period
ANSWER
$3100
EXPLANATION
Sally deposits $2500 at 8% interest for 3 years.
We want to find the amount she can withdraw at the end of the period.
To know this, we have to first find the interest.
Simple Interest is given as:
[tex]\begin{gathered} SI\text{ = }\frac{P\cdot\text{ R }\cdot\text{ T}}{100} \\ \text{where P = principal = \$2500} \\ R\text{ = rate = 8\%} \\ T\text{ = 3 years} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} SI\text{ = }\frac{2500\cdot\text{ 8 }\cdot\text{ 3}}{100} \\ SI\text{ = }\frac{60000}{100} \\ SI\text{ = \$600} \end{gathered}[/tex]Therefore, after 3 years the interest will be $600.
The amount she can withdraw after this period is therefore the sum of the principal and the interest:
$2500 + $600 = $3100
She can withdraw $3100 at the end of the period.
In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of 1/2, reflected4 across the x-axis, and movedthrough the translation [? ].
We have to identify the translation.
We can see that the green triangle represents the transformation of triangle ABC after a dilation with a scale factor of 1/2 and a reflection across the x-axis.
We can then find the translation in each axis from the image as:
Triangle is DEF is translated 3 units to the left (and none in the vertical axis).
We can express this translation as this rule:
[tex](x+3,y+0)[/tex]Answer: (x+3, y+0)