Answer: She should use 25 millimeters of substance A
This is a case of ratio. Substance A and B are to be mixed in a given ratio such that as A increases, B would similarly increase, not by the same quantity but by the same ratio. That means every time you add 5 parts of A, you need to add 3 parts of B. In effect, if you add 5 parts of A ten times (5 * 10 = 50 parts) you will need to add 3 parts of B ten times also (3 * 10 = 30).
So the
Х101112y27a11In order for the data in the table to represent a linearfunction with a rate of change of -8, what must be thevalue of a?a = 2O a = 3a = 19O a = 35
Answer:
a = 19
Explanation
First, note that the rate of change of a linear function is known as its slope.
Given the coordinates (x1, y1) and (x2, y2), the formula for calculating the slope is expressed as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the coordinates (10, 27) and (11, a) where m = -8, substitute the values into the formula;
[tex]\begin{gathered} \frac{a-27}{11-10}=-8 \\ \frac{a-27}{1}=-8 \\ a-27=-8 \end{gathered}[/tex]Add 27 to both sides as shown;
[tex]\begin{gathered} a-27+27=-8+27 \\ a=27-8 \\ a=19 \end{gathered}[/tex]Hence the value of a is 19
What is the slope of the line that contains the points ( -2 , 1 ) and ( 4 , -2 )?
Answer
Slope
Step-by-step explanation:
Given the following points of the line, (-2, 1) and (4, -2)
Slope = rise / run
Rise = y2 - y1
Run = x2 - x1
Hence, slope = y2 - y1/ x2 - x1
From the given points
let x1 = -2, y1 = 1, x2 = 4 and y2 = -2
Slope = -2 - 1 / 4 - (-2)
Slope = -3 / 4 + 2
Slope = -3 / 6
Slope = -1/2
Hence, the slope of the line that contains the two points is -1/2
Select all polynomials that are divisible by (x-1)
Explanation
[tex]\begin{gathered} \frac{5x^4+9}{x} \\ \end{gathered}[/tex]Step 1
Split the fraction
[tex]\frac{5x^4+9}{x}=\frac{5x^4}{x}+\frac{9}{x}[/tex]Step 2
Simplify:
[tex]\begin{gathered} \frac{5x^4}{x}+\frac{9}{x}=5x^{4-1}\text{ +}\frac{9}{x\text{ }} \\ \frac{5x^4}{x}+\frac{9}{x}=5x^3\text{ +}\frac{9}{x\text{ }} \\ 5x^3\text{ +}\frac{9}{x\text{ }} \end{gathered}[/tex]so,the answer is
[tex]5x^3\text{ +}\frac{9}{x\text{ }}[/tex]I hope this helps you
Find the modes for the data in the given frequency distribution. (Round your answers to one decimal place. If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)Points Scored in Basketball Game Frequency 3 9 7 5 8 9 10 4 13 1 15 2 17 1
SOLUTION
The mode of a distribution is the data with the highest frequency or the data that occure most in the distribution.
Consider the distribution given
The highest frequency is
[tex]9[/tex]The data with this frequency are two which are
[tex]\begin{gathered} 3 \\ \text{and } \\ 8 \end{gathered}[/tex]Therefore
The mode of the distribution is 3,8
Answer: Mode is 3,8
Identify the domain of the function represented below:y= 2√x4-3x ≥ 4O x ≥ 3Ox≥-3Ο x > 0
Solution
Step 1
Write the function
[tex]y=2\sqrt{x-4}-3[/tex]Step 2
[tex]\begin{gathered} \mathrm{Domain\:definition} \\ The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values \\ \:for\:which\:the\:function\:is\:real\:and\:defined. \end{gathered}[/tex]Step 3
To find the function domain, equate the expression in the square to at least zero.
[tex]\begin{gathered} x\text{ - 4 }\ge\text{ 0} \\ \\ x\text{ }\ge\text{ 4} \end{gathered}[/tex]Final answer
[tex][/tex]Anao Savings and Loan is paying 6% interest compounded quarterly. Find the future value of ₱1,000, deposited at the beginning of every 3 months, for 5 years.
$1346.86
1) Having these data, we can write out the following:
6% interest compounded quarterly
Present Value: 1,000
5 years
2) Let's plug into the formula below:
[tex]\begin{gathered} F=P(1+\frac{r}{n})nt \\ F=1000(1+\frac{0.06}{4})^{4\cdot5} \\ F=1346.8555\approx1346.86 \end{gathered}[/tex]Notice the rate is given in the decimal form. N stands for the number of periods that it is compounded.
3) Hence, the future value is: $1346.86 approximately
I need help finding the answer. I don't need astep-by-step explanation just the answer please.Thank you.
Find a using the theorem of sinus:
[tex]\sin(57°)=\frac{a}{29}[/tex][tex]a=\sin(57)*29=24.32[/tex]Now with the Pythagoras theorem find b:
[tex]a^2+b^2=29^2[/tex][tex]24.32^2+b^2=29^2[/tex][tex]b^2=29^2-24.32^2[/tex][tex]b^2=841-591.46[/tex][tex]b=\sqrt{841-591.46}=\sqrt{249.53}[/tex][tex]b=15.79[/tex]Finally, find B knowing that the sum of all internal angles of a triangle is equal to 180°:
[tex]B=180-57-90=33°[/tex]A football team is on their own 45 yard line. Theu lose an average of 6 yards on the next three plays. What yard line the team on after the three plays?
39 yard lines
Explanations:The initial yard line = 45 yards
Average amount of yards lost after 3 plays = 6 yards
The yard line after the three plays = 45 - 6
The yard line after the three plays = 39 yards
The team are on the 39 yard line after the three plays
Graph the system of equation on the grid below in the mark their point of intersections (point c )y = 3x + 3y = x + 5
Given
y=3x+3
y=x+5
Procedure
Solve for x. 2 - In(x + 3) = In 4 O x= In 4-1 O x = 2e x=2-3 X = -3
Starting with the equation:
[tex]2-\ln (x+3)=\ln (4)[/tex]Add ln(x+3) to both sides:
[tex]2=\ln (4)+\ln (x+3)[/tex]Use the property:
[tex]\ln (a)+\ln (b)=\ln (a\cdot b)[/tex]to rewrite the right hand side of the equation:
[tex]2=\ln (4(x+3))[/tex]Use the distributive property to rewrite 4(x+3) as 4x+12:
[tex]2=\ln (4x+12)[/tex]Use the property:
[tex]a=b\Rightarrow c^a=c^b[/tex]for a=2, b=(4x+12) and c=e:
[tex]e^2=e^{\ln (4x+12)}[/tex]Use the property:
[tex]e^{\ln (a)}=a[/tex]to rewrite the right hand side of the equation:
[tex]e^2=4x+12[/tex]Substract 12 from both sides of the equation:
[tex]e^2-12=4x[/tex]Divide both sides by 4:
[tex]\frac{e^2}{4}-3=x[/tex]Substitute the value of x into the original equation to check the answer.
Macmillan Learning
Suppose that your federal direct student loans plus accumulated interest total $33,000 at the time that you start repayment and the interest rate on all the loans is 5.23%.
(a) If you elect the standard repayment plan of a fixed amount each month for 10 years, what would your monthly payment be?
(b) How much would you pay in interest over the 10 years?
Using the monthly payment formula, it is found that:
a) Your monthly payment would be of $353.74.
b) You would pay $9,444.8 in interest over the 10 years.
What is the monthly payment formula?The monthly payment rule is presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the meaning of each parameter is given as follows:
P is the initial amount.r is the interest rate.n is the number of payments.In the context of this problem, the values of these parameters are:
P = 33000, r = 0.0523, r/12 = 0.0523/12 = 0.00435833, n = 10 x 12 = 120.
Hence the monthly payment is calculated as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 33000\frac{0.00435833(1.00435833)^{120}}{(1.00435833)^{120} - 1}[/tex]
A = $353.74.
The total amount paid is:
T = 120 x 353.74 = $42,444.8.
The interest paid is the total amount subtracted by the loan value, hence:
42444.8 - 33000 = $9,444.8.
More can be learned about the monthly payment formula at https://brainly.com/question/14802051
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solve the equations. 12x - 5y = -20y= x + 4 x=y=
We can substitute the second equation in the first one
[tex]\begin{gathered} 12x-5(x+4)=-20 \\ 12x-5x-20=-20 \\ 7x=0 \\ x=0 \end{gathered}[/tex]Since x=0, then
[tex]\begin{gathered} y=0+4 \\ y=4 \end{gathered}[/tex]to be sure, we replace the result in the first equation
[tex]12(0)-5(4)=0-20=-20[/tex]Then the answer is x=0, y=4
Exercises 12.3 Complete the following: 1. Complete the squares for each quadratic, list the center labeling its translated center: (a) x2 + 2x + y2 – 4y = 4 (c) 2x2 + 2y2 + 3x - 5y = 2 (e) x2 + y2 + 3x = 4 (g) x2 + y2 + 4x = 0 (i) x2 + y2 + 2mx 2ny = 0 (b) (d -Letter g
Answer:
(x + 2)² + y² = 4
Explanation:
If we have an equation with the form:
x² + bx = c
We can complete the square by adding (b/2)² to both sides.
In this case, we have:
x² + y² + 4x = 0
So, we can organize the terms as:
(x² + 4x) + y² = 0
Therefore, to complete the square of (x² + 4x) we need to add:
[tex](\frac{b}{2})^2=(\frac{4}{2})^2=2^2=4[/tex]Then:
(x² + 4x + 4) + y² = 0 + 4
(x + 2)² + y² = 4
On the other hand, the equation of a circumference is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) is the center and r is the radius.
So, we can rewrite the equation as:
(x + 2)² + y² = 4
(x -(-2)² + (y - 0)² = 2²
Therefore, the center is the point (-2, 0) and the radius is 2. So, the graph of the circle is:
Page 112 question 7 part 8 which equation matched the following graph A f(x)=2^xBf(x)=-2^xC f(x)=-2^xDf(x)=-3x2^x
EXPLANATION
The given graph corresponds to the function f(x)= -2^x
A certain forest covers an area of 4000km ^ 2 Suppose that each year this area decreases by 5.5%. What will the area be after 12 years?Use the calculator provided and round your answer to the nearest square kilometer.
In order to calculate the area after 12 years, let's use the following exponential model:
[tex]A=A_0\cdot(1+r)^t[/tex]Where A is the area after t years, A0 is the initial area and r is the rate of increase or decrease.
So, for A0 = 4000, r = -0.055 and t = 12, we have:
[tex]\begin{gathered} A=4000\cdot(1-0.055)^{12} \\ A=4000\cdot0.945^{12} \\ A=4000\cdot0.50720287 \\ A=2028.8 \end{gathered}[/tex]Rounding to the nearest km², the area is 2029 km².
Aiden is making a cookie recipe that requires 4 cups of sugar for every 8 cups of flour. Aiden only has 6 cups of flour. He concludes that he will only need 2 cups of sugar. Is Aiden correct? Why or why not?A Aiden is incorrect. He needs 4 cups of sugar because decreasing the number of cups of flour by 2 requires increasing the number of cups of sugar by 2.B Aiden is correct. The number of cups of sugar must be reduced by 2 because the number of cups of flour is reduced by 2.C Aiden is correct. Half the amount of sugar is needed because only half of the recipe will be made.D Aiden is incorrect. He needs 3 cups of sugar because the ratio 3:6 is equivalent to 4:8.
Aiden is incorrect. He needs 3 cups of sugar
Austin’s taxi charges $5 plus $0.30 per mile for fare in a city. Sylvia’s taxi charges $8 plus $0.20 per mile for fare in the city. What will be the linear equation for the charges if you use Austin’s taxi?
austins taxi charges a flat fee of 5 + 0.3 per mile, so
y = 0.3x + 5
B
need help asap got something I dont understand
Formula
[tex]\text{ Area = }\frac{B\text{ + b}}{2}\text{ h}[/tex]B = long base
b = short base
h = height
Counting the number of squares:
B = 8
b = 6
h = 4
Substitution
[tex]\begin{gathered} \text{ Area = }\frac{(8\text{ + 6)}}{2}4 \\ \text{ Area = }\frac{14}{2}4 \\ Area=\frac{56}{2}\text{ } \\ \text{Area = 28} \end{gathered}[/tex]The absolute value of a negative number will alwats be a positive number. True or false.
The absolute value of a number indicates the distance of a number from zero.
It can simply be said to be the non-negative value of a number without reagrds to the sign of the number.
The absolute value is written in the form:
|-a| = a
|a| = a
|-6| = 6
|5| = 5
Therefore, the absolute value of a negative number will always be a positive number. This
Brooke Puts 400.00 into an account to use for school expenses the account earns 14%interest compounded quarterly how much will be in the account after 5 years
According to the problem, the principal is 400, the interest rate is 14%, the time is 5 years, and it's compounded quarterly which means there are 4 compound periods each year.
We have to use the compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Replacing the given values, we have.
[tex]\begin{gathered} A=400(1+\frac{0.14}{4})^{4\cdot5} \\ A=400(1+0.035)^{4\cdot5} \\ A=400(1.035)^{20} \\ A\approx795.92 \end{gathered}[/tex]Hence, after 5 years, there will be $795.92, approximately.the shaded triangle is inside a square which has side lengths of 10 inches.answer choices (select all that apply)A) the shaded triangle inside the square has a base and height of 10 inches.B) since the square has an area of 100in., the shaded triangle also has an area of 100in².C)the area of the shaded triangle can be determined by adding it's base, 10 inches, to its lengths, 11 inches and 12 inches.D)since the square has an area of 100 in²., the shaded triangle has an area which equals half the area of the square, 50 in².
The correct options are options A and D
The shaded triangle inside the square has a base and height of 10 inches.
And
Since the square has an area of 100 in²., the shaded triangle has an area which equals half the area of the square, 50 in².
Solve the following system of equations using an inverse matrix. You must alsoindicate the inverse matrix, A-1, that was used to solve the system. You mayoptionally write the inverse matrix with a scalar coefficient.2x-3y = -55x - 4y = -2Al=y =
The two equations given are:
[tex]\begin{gathered} 2x-3y=-5 \\ 5x-4y=-2 \end{gathered}[/tex]The coefficient matrix A is:
[tex]A=\begin{bmatrix}2 & -3 \\ 5 & -4\end{bmatrix}[/tex]The variable matrix X is:
[tex]X=\begin{bmatrix}x \\ y\end{bmatrix}[/tex]and the constant matrix B is:
[tex]B=\begin{bmatrix}-5 \\ -2\end{bmatrix}[/tex]Then, AX = B looks like,
[tex]\begin{gathered} AX=B \\ X=A^{-1}B \end{gathered}[/tex]So, the variables "x" and "y" are found my multiplying the inverse of A by the matrix B.
Let's find the inverse matrix of A:
Given, a 2 x 2 matrix,
[tex]A=\begin{bmatrix}a & b \\ c & d\end{bmatrix}[/tex]The inverse of this matrix will be,
[tex]A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}[/tex]Using the formula, we have:
[tex]\begin{gathered} A^{-1}=\frac{1}{-8--15}\begin{bmatrix}-4 & 3 \\ -5 & 2\end{bmatrix} \\ =\frac{1}{7}\begin{bmatrix}-4 & 3 \\ -5 & 2\end{bmatrix} \\ =\begin{bmatrix}-\frac{4}{7} & \frac{3}{7} \\ -\frac{5}{7} & \frac{2}{7}\end{bmatrix} \end{gathered}[/tex]Now, we can solve for the matrix X, shown below:
[tex]X=\begin{bmatrix}-\frac{4}{7} & \frac{3}{7} \\ -\frac{5}{7} & \frac{2}{7}\end{bmatrix}\begin{bmatrix}-5 \\ -2\end{bmatrix}=\begin{bmatrix}(-\frac{4}{7})(-5)+(\frac{3}{7})(-2) \\ (-\frac{5}{7})(-5)+(\frac{2}{7})(-2)\end{bmatrix}=\begin{bmatrix}\frac{20}{7}-\frac{6}{7} \\ \frac{25}{7}-\frac{4}{7}\end{bmatrix}=\begin{bmatrix}\frac{14}{7} \\ \frac{21}{7}\end{bmatrix}=\begin{bmatrix}2 \\ 3\end{bmatrix}[/tex]The solution matrix, X, is
[tex]X=\begin{bmatrix}2 \\ 3\end{bmatrix}[/tex]This, means the solution to the system of equations is:
[tex]x=2,y=3[/tex]Number 4 i need help no it’s due at 9:00
When we have a negative sign in front of a number, the sign of the number is changed, therefore if the number is negative the number will turn positive. This is done below:
[tex]\begin{gathered} (-4)\text{ - (-5)} \\ (-4)\text{ + 5} \end{gathered}[/tex]When we sum two numbers of different signs, we subtract their values and maintain the sign of the greatest one:
[tex]-4\text{ + 5 = 1}[/tex]Give the side lengths in order from least to greatest. The side lengths are LM, MK, LK.
Answer
The order of this lengths from least to greates
MK < LM < LK
Explanation
To answer this, we need to first find the measure of the third angle to know this order.
Sum of angles in a triangle is 180°.
Third angle + 57° + 64° = 180°
Third angle + 121° = 180°
Third angle = 180° - 121°
Third angle = 59°
So, for the lengths of the sides, the length of the side is determined by the angle that is facing that side.
So, the bigger the angle, the bigger the side opposite that angle.
LM - 59°
MK - 57°
LK - 64°
We know that
57° < 59° < 64°
So,
MK < LM < LK
Hope this Helps!!!
step 3 find the mean of all the squared deviations step 4 take the square root of the mean of the squared deviations
Explanation
Step 3: Find the mean of all squared deviations.
[tex]\operatorname{mean}\text{ squared deviation }=\frac{25+25+0+4+4+0}{6}=\frac{58}{6}=9.67[/tex]Step 4: Take the square root of the mean of the squared deviations (from step 3)
[tex]\text{standard deviation }=\sqrt[]{mean\text{ squared deviation}}=\sqrt[]{9.67}=3.11[/tex]Note that the average distance between individual data values and the mean is simply called standard deviation.
Therefore the average distance between individual data values and the mean is 3.11
In 2012, the population in atown was 8,000 people. In2017, the population was11,400. What was thepercent increase in thepopulation?
1. first we determine the growth in that period of time, for which we find a difference that in 5 years there was an increase of 3,400 people
[tex]\begin{gathered} 2012=8.000\text{ people} \\ 2017=11.400\text{ people} \\ \text{the growth in 5 years } \\ 11.400-8000=3.400 \end{gathered}[/tex]now we divide that increment by the initial value, to get the percentage of increase;
[tex]\begin{gathered} 3.400/8.000=0.425\text{ percent increase in the population} \\ \end{gathered}[/tex]In a factory, the number of products produced by the workers on the second shift is twice the number of products produced by the first shift. Illustrate this relationship graphically. (Hint: Let x stand for the number of products produced by the first shift, and let y stand for the number of products produced by the second shift.)
To answer this question, we have:
1. Let x stand for the number of products produced by the first shift.
2. Let y stand for the number of products produced by the second shift.
If we have:
Then, we can write it algebraically as follows:
[tex]y=2x[/tex]And we can represent this relationship graphically by giving values for x, then applying the rule of the relation, and finally having the corresponding values for y.
If we suppose that workers belonging to the first shift produced:
• x = 0 products.
,• x = 10 products.
,• x = 20 products.
,• x = 30 products.
,• x = 40 products.
,• x = 50 products.
Then, we have that the second shift will produce:
[tex]\begin{gathered} x=10\Rightarrow y=2x\Rightarrow y=2(10)=20 \\ x=20\Rightarrow y=2(20)\Rightarrow y=40 \\ x=30\Rightarrow y=2(30)\Rightarrow y=60 \\ x=40\Rightarrow y=2(40)\Rightarrow y=80 \\ x=50\Rightarrow y=2(50)\Rightarrow y=100 \\ x=0\Rightarrow y=2(0)\Rightarrow y=0 \end{gathered}[/tex]Therefore, we can graph the relationship using the next coordinate pairs - we can start by (0, 0) - in this case, none of the workers produced any products):
• (0, 0)
,• (10, 20)
,• (20, 40)
,• (30, 60)
,• (40, 80)
,• (50, 100)
In this case, we can see that we are assuming that the number of products is positive integers (or natural numbers), and the relationship is discrete (not continuous) between the values for the first and second shift (that is why we do not a continuous line between the points.)
In other words, we can draw both functions for natural numbers in both axes. The y-axis will be twice in value as the values in the x-axis, and as a real ca
tionables wiin two-step rulesFill in the table using this function rule.y=2x+3Xv2D6DIDIOD810
Evaluating a function means finding the value of a function that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned.
Our function is
[tex]y=2x+3[/tex]For the given values on the table, we have the corresponding y values
[tex]\begin{gathered} y(2)=2\cdot(2)+3=4+3=7 \\ y(6)=2\cdot(6)+3=12+3=15 \\ y(8)=2\cdot(8)+3=16+3=19 \\ y(10)=2\cdot(10)+3=20+3=23 \end{gathered}[/tex]Select the statement that describes the inequality:n < = 9.25 Question 3 options:A number is no less than 9.25.A number is no more than 9.25.A number is below 9.25.A number exceeds 9.25.
Solution:
Given the inequality below;
[tex]n\leq9.25[/tex]The inequality sign in the above expression means less than or equal to, i.e.
[tex]n\text{ is no more than 9.25}[/tex]Hence, the statement that describes the inequality is
A number is no more than 9.25.
I need help understanding how to compare irrational numbers and multiplication of exponents. Can you help?
1) A good way to compare irrational numbers is by their approximate value. For example, let's pick two irrational numbers:
π and √2 Two irrational numbers
The value of each approximately is
3.14 and 1.41 so
3.14 > 1.41
And this principle fits for the other irrational numbers.
2) Multiplication of exponents
If we have two powers and we have to operate them, we'll proceed this way:
[tex]\begin{gathered} (a^3)^6=a^{3\cdot6}=a^{18} \\ a^3\cdot a^6=a^{3+6}=a^9 \end{gathered}[/tex]