Answer:
Option 3
Explanation:
If the employees are assigned to one of four pay scales. Randomly selecting a pay scale and surveying every employee in that pay scale will result in undercoverage since employees in every other pay scale are excluded.
Hello can you please help me with question number 11
To find the fraction which is greater than 50%:
Let us find the percentage value for all the options.
a.
[tex]\begin{gathered} \frac{2}{3}\times100\text{ \%}=\frac{200}{3} \\ =66.66\text{ \%} \end{gathered}[/tex]b.
[tex]\begin{gathered} \frac{2}{5}\times100\text{ \%}=\frac{200}{5} \\ =40\text{\%} \end{gathered}[/tex]c.
[tex]\begin{gathered} \frac{12}{20}\times100\text{ \%}=\frac{1200}{20} \\ =60\text{ \%} \end{gathered}[/tex]Hence, options (a) and (c) have a fraction is greater than 50%.
The formula shows that A, the area of a square, depends on s, the length of the sides of a square. A = s². What is the independent variable in the formula?
A variable is called independent when its value is independent of other variables.
For example, the side length doesn't depend on the area value.
A variable is dependent when its value is dependent of other variables.
For example, the area value depends on the side length value.
Therefore, in the formula A = s², the independent variable is s.
O GEOMETRY Pythagorean Theorem For the following right triangle, find the side length x. Round your answer to the nearest hundredth. 10 X Ú
ANSWER
x = 8
EXPLANATION
Here we have a right triangle. The lengths of two sides are given and we have to find the length of the third side. To do so, we will use the Pythagorean Theorem,
[tex]c^2=a^2+b^2[/tex]Where a and b are the legs, and c is the hypotenuse.
The hypotenuse of a right triangle is always the longest side, which is the side opposite to the right angle. In this case, the hypotenuse is 10 units long, one of the legs is 6 units long and we have to find the length of the other leg, x,
[tex]10^2=x^2+6^2[/tex]Solving for x,
[tex]x=\sqrt{10^2-6^2}=\sqrt{100-36}=\sqrt{64}=8[/tex]Hence, the value of x is 8.
at a given time of day, the ratio of the height of an object to the length of its shadow. is the same for all objects. if a 4-ft stick in the ground casts a shadow of 0.8ft, find the height if a tree that casts a shadow is 7.66 ft.
Stick -- Height 4 ft ---Shadow 0.8 ft
Tree---Height x ft --- Sadow 7.66 ft
We have a relation of equivalence, so the height of the tree x can be calculated as
[tex]x=\frac{7.66\cdot4}{0.8}=38.3\text{ ft}[/tex]The height of the tree is 38.3 ft
3 Neil brought 2 pounds of grapes for fruit salad at the class picnic. There are 8 ounces of grapes left. How many ounces of grapes were used? Look at the lable in problem 4 to help you answer the question
1 pound is equal to 16 ounces.
It is given that Neil brought 2 pounds of grapes.
Convert into ounces
2 pounds=32 ounces.
It is also given that 8 ounces of grapes left.
The ounces of grapes that were used are
32-8=24 ounces.
Hence there are 24 ounces of grapes were used.
Solve the follow system of equations using substitution: x - 5y = 0-x + 5y = 3
Given the system of equations below
[tex]\begin{gathered} x-5y=0\text{ (1)} \\ -x+5y=3\text{ (2)} \end{gathered}[/tex]Using substitution method:
From equation (1), make x the subject
[tex]\begin{gathered} x-5y=0 \\ x=5y \end{gathered}[/tex]Substitute 5y for x into equation (2)
[tex]\begin{gathered} -x+5y=3 \\ \text{Substitute 5y for x into equation (2) above} \\ -(5y)+5y=3 \\ -5y+5y=3 \\ 0\ne3 \end{gathered}[/tex]Since, the values of x and y can not be determined
Hence, there is no solution to the given system of equations.
Solve for x, y, and z,1 -6 -81 -72) 10 1 80 0 1 30
The system, it is standard form is
meaning
[tex]y=8[/tex]and
[tex]z=3.[/tex]With the value of y an z in hand, we now solve for x in the first equation
[tex]x-6(8)-8(3)=-7[/tex][tex]x=-7+48+24[/tex][tex]\textcolor{#FF7968}{\therefore x=65.}[/tex]Hence, the solution is
x = 65, y = 8, and z = 3.
Round answers to the nearest cent. 1. John is going to invest $100 in an account for 3 years. If the account earns 6% simple interest, how much interest can he expect to earn?
Data:
Principal: $100
Time: 3 years
Simple interest: 6%
You can find the interest John earn whit the next formula for simple interest:
[tex]I=P\cdot r\cdot t[/tex]
P is principal, r is the rate of interest in decimals and t is time.
[tex]\begin{gathered} I=100\cdot\frac{6}{100}\cdot3 \\ \\ I=18 \end{gathered}[/tex]Then, John will earn $18 after 3 years(-t) • (-t) • (-t) • (-t) • (-t)
Remember that when two negative numbers are multiplied, the result is positive, while if a negative number is multiplied by a positive number, the result is negative.
If an expression has an even amount of negative factors, then the product is positive. If an expression has an odd amount of negative factors, then the product is negative.
In the given expression:
[tex](-t)\cdot(-t)\cdot(-t)\cdot(-t)\cdot(-t)[/tex]There are five negative factors. Then, the result must be negative. Recalling the properties of exponentials, we can rewrite this expression as:
[tex](-t)\cdot(-t)\cdot(-t)\cdot(-t)\cdot(-t)=(-t)^5[/tex]Which is equal to:
[tex]-t^5[/tex]Therefore:
[tex](-t)\cdot(-t)\cdot(-t)\cdot(-t)\cdot(-t)=-t^5[/tex]Given: AABC = ADEFDetermine the perimeter of A ABC.A) 13 units B) 28 units C) 39 units D) 42 units
1) Given these two congruent triangles, we have a right triangle. So we can use the metric relations for the right triangle
2) So we can write for the triangle ΔDBC, let's find the leg DB
a²=b²+c²
BC²=DC²+DB² BC is the hypotenuse from ΔDBC
15²= 12² +DB²
225= 144 +DB² Flip it
DB²=225-144
√DB²=√81
DB =9
If AB = 14, DB = 9 then DA = 14-9 DA = 5
Now let's find the hypotenuse from
what is 10x^2 +79x-8
Factor:
The coefficient of x² is 10 and the constant term is -8, so:
[tex]10\times-8=-80[/tex]The factors of 80 which sum to 79 are -1 and 80, hence:
[tex]10x^2+79x-8=10x^2+80x-x-8[/tex]Group like terms:
[tex]10x^2+80x-x-8=8(10x-1)+x(10x-1)[/tex]Factor 10x-1 from the previous expression:
[tex](10x-1)(8+x)[/tex]F-LE.1c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 1. The table below shows how the expected values of a computer and a printer vary with time. Time (years after purchase) Value of Computer Value of Printer 0 $960 $300 $720 $240 2 $540 $180 3. $405 $120 Based on the data in the table, which of the two devices decays in expected value by a constant
When a quantity changes by a constant rate we can fit the data of the quantity with a line, then by plotting the given data we can see which of the two devices decays in expected value by a constant, like this:
• For the variable "value of computer"
• For the variable "Value of printer"
As you can see, when we graph the data in the table, we can see that the value of the printer varies linearly in terms of time, then this device decays by a constant value.
Then, the answer is the printer
5. Write a simplified expression for the perimeter of a rectangle with length 5x+2 and width 6x+8Write answers in standard form.I
Length of the Rectangle = 5x+2
Width of the rectangle = 6x+8
Perimeter of a rectangle = 2(Length + Width )
Therefore:
[tex]\begin{gathered} \text{Perimeter}=2(5x+2+6x+8) \\ =2(5x+6x+2+8) \\ =2(11x+10) \\ =22x+20 \end{gathered}[/tex]The perimeter of the rectangle in simplified standard form will be:
[tex]Perimeter=2(11x+10)\text{ Units}[/tex]the questions says given vertices ABC which with the following vertices(4,8) b(1,5) and c (6,3) .which of the following are coordinates of the vertices of A'B'C after reflection across y=2 is applied?
Let's draw a diagram to represent the given situation.
The image below shows the triangle ABC and the line y = 2.
We just have to draw one symmetric triangle under the line y = 2.
Are you can observe in the image above, the vertices of the reflection are: A'(4, -4), B'(1, -1), and C'(6, 1).
Therefore, the right answer is B.Answer: B
Step-by-step explanation: Let's draw a diagram to represent the given situation.
The image below shows the triangle ABC and the line y = 2.
We just have to draw one symmetric triangle under the line y = 2.
Are you can observe in the image above, the vertices of the reflection are: A'(4, -4), B'(1, -1), and C'(6, 1).
2. The temperature on Monday was 16.3 degrees and on Tuesday it was 3 degrees colder. What was the temperature on Tuesday? Show your work on the number line below.
We have that the temperature on monday was 16.3 degrees, then on tuesday we have:
[tex]\begin{gathered} \text{ Tuesday's Temperature: Monday's temperature - 3} \\ \Rightarrow16.3-3=13.3 \end{gathered}[/tex]Therefore, the temperature on Tuesday was 13.3, and we can see the change in the number line like this:
Barry has 17 more than two-thirds of the number of cards in his brother's baseball card collection. If x represents thenumber of baseball cards his brother has, which expression represents the number of baseball cards Barry has?o 17x - 2 3o 17x + 2 }
Given, x represents thenumber of baseball cards Barry's brother
answer the following question .
If two lines are perpendicular, then:
[tex]m1\times m2=-1[/tex]From the equation:
[tex]y=-\frac{1}{3}x-5[/tex]We can conclude:
[tex]m1=-\frac{1}{3}[/tex]So:
[tex]\begin{gathered} -\frac{1}{3}\times m2=-1 \\ m2=3 \end{gathered}[/tex]Let:
[tex](x1,y1)=(0,-3)[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m2(x-x1) \\ y-(-3)=3(x-0) \\ y+3=3x \\ solve_{\text{ }}for_{\text{ }}y\colon \\ y=3x-3 \end{gathered}[/tex]Given: Q is between R and SWhich conclusion and associated reason is valid?A.)RQ+QS=RS, by the segment addition postulate B.) RS+RQ=QS, by the segment addition postulateC.) Q is the bisector of , the definition of bisector D.) RQ=QA by the segment addition postulate
From the given problem, Q is between R and S
Segment RQ + Segment QS = Segment RS
The answer is Choice A.
Determine the concavity of the graph of f(x) = 8 - x^2 between x = -1 and x = 5 by calculating average rates of change over intervals of length 2.a) The average rate of change over the interval -1 ≤ x ≤ 1 =b) The average rate of change over the interval 1 ≤ x ≤ 3=c) The average rate of change over the interval 3 ≤ 2 ≤ 5 =
Given the function below
[tex]f(x)=8-x^2[/tex]To determine the concavity of the graph of the given function
We calculate the average rate change of the given interval
The formula to find the average rate of change, A(x), change is
[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]a) For the interval -1 ≤ x ≤ 1, the average rate of change, A(x) is
[tex]\begin{gathered} A(x)=\frac{f(b)-f(a)}{b-a} \\ \text{Where a}=-1,b=1,f(x)=8-x^2 \\ A(x)=\frac{(8-(1)^2)-(8-(-1)^2)}{1-(-1)}=\frac{(8-1)-(8-1)}{1+1}=\frac{7-7}{2}=\frac{0}{2}=0 \end{gathered}[/tex]Hence, the average rate change over the interval -1 ≤ x ≤ 1 is 0
b) For the interval 1 ≤ x ≤ 3, the average rate of change, A(x) is
[tex]\begin{gathered} A(x)=\frac{f(b)-f(a)}{b-a} \\ \text{Where a}=1,b=3,f(x)=8-x^2 \\ A(x)=\frac{(8-(3)^2)-(8-(1)^2)}{3-1} \\ A(x)=\frac{(8-9)-(8-1)}{2} \\ A(x)=\frac{-1-(7)}{2} \\ A(x)=\frac{-8}{2} \\ A(x)=-4 \end{gathered}[/tex]Hence, the average rate change over the interval 1 ≤ x ≤ 3 is -4
c) For the interval 3 ≤ x ≤ 5, the average rate of change, A(x) is
[tex]\begin{gathered} A(x)=\frac{f(b)-f(a)}{b-a} \\ \text{Where a}=3,b=5,f(x)=8-x^2 \\ A(x)=\frac{(8-(5)^2)-(8-(3)^2)}{5-3} \\ A(x)=\frac{(8-25)-(8-9)}{2} \\ A(x)=\frac{-17-(-1)}{2} \\ A(x)=\frac{-17+1}{2} \\ A(x)=\frac{-16}{2} \\ A(x)=-8 \end{gathered}[/tex]Hence, the average rate change over the interval 3 ≤ x ≤ 5 is -8
d) From the above deductions, the average rate of change is decreasing.
Hence, the graph of the function f(x) is Concave down
Solve ln(3x+4)−3ln(3)=ln(2x+1). Round answers to nearest hundredth.
We can operate on that expression as shown below
[tex]\begin{gathered} \ln (3x+4)-3\ln (3)=\ln (2x+1) \\ \Rightarrow\ln (3x+4)-\ln (3^3)=\ln (2x+1);\ln (z^y)=y\cdot\ln (z) \\ \Rightarrow\ln (\frac{3x-4}{3^3})=\ln (2x+1);\ln (\frac{z}{y})=\ln (z)-\ln (y) \end{gathered}[/tex]Remember that the function 'ln' is injective.This means that,
[tex]\ln (z)=\ln (y)\Rightarrow z=y;y,z\in(0,\infty)[/tex]So,
[tex]\begin{gathered} \ln (\frac{3x-4}{3^3})=\ln (2x+1) \\ \Rightarrow\frac{3x-4}{3^3}=2x+1 \\ \Rightarrow\frac{3x-4}{27}=2x+1 \end{gathered}[/tex]And this is simply a usual equation with one unknown. Solving for x,
[tex]\begin{gathered} \frac{3x-4}{27}=2x+1 \\ \Rightarrow2x-\frac{1}{9}x=\frac{4}{27}-1 \\ \Rightarrow\frac{17}{9}x=-\frac{23}{27} \\ \Rightarrow x=-\frac{23}{51} \end{gathered}[/tex]Now, we need to round to the nearest hundredth
[tex]\begin{gathered} x=-\frac{23}{51}=-0.4209\ldots \\ x\approx-0.45 \end{gathered}[/tex]Thus, the answer is x=-0.45 once we have rounded it
use a formula for the quadratic function depicted in the following graph
Step 1
From the graph, the zeroes of the quadratic function are;
[tex]\begin{gathered} x=-1 \\ x=4 \end{gathered}[/tex]Step 2
Find the formula for the quadratic function in the graph.
[tex]\begin{gathered} x+1=0 \\ x-4=0 \\ (x+1)(x-4) \\ x^2-4x+x-4 \\ x^2-3x-4 \end{gathered}[/tex]Hence the formula for the quadratic function graphed is
[tex]x^2-3x-4[/tex]Which of these three dimensional figures pairs have no vertices
In the question we are asked to find which of the three dimensional figures have no vertices.
Explanation
In the options, we are given the following shapes, cone , pyramid, circle, sphere, cylinder.
In the above only two options are placed together and have no vertices.
Answer: cylinder and sphere
Today only, a desk is being sold at a 35% discount. The sale price is $429.What was the price yesterday?
Given:
The discount for the desk today, D=35%.
The sale price, SP=$429.
The expression for sale price is,
[tex]SP=\frac{100-D}{100}\times CP[/tex]Here, CP is the price yesterday.
Substitute the known values and solve for CP.
[tex]\begin{gathered} 429=\frac{100-35}{100}\times CP \\ 429=\frac{65}{100}\times CP \\ CP=\frac{429\times100}{65} \\ CP=660 \end{gathered}[/tex]Therefore, the price yesterday is $660.
75 quarters, 20 dimes, and 123 pennies are in a bag. What is the probability of pulling a dime out of the bag? O 9.2% O 11.7%
How many dimes are in 75 quarters?
75 quarters x 25 cents
= 1875 cents
1875 cents / 10 cents
= 187.5 dimes
How many dimes are in 123 pennies?
A dime is worth 10 cents and is equal to 2 nickels or 10 pennies
For 123 pennies, we have : 123 / 10 = 12.3 dimes
75 quarters + 20 dimes + 123 pennies = 187.5 dimes + 20 dimes
+ 12. 3 dimes = 219. 8 dimes
What is the probability of pulling a dime out of the bag?
20 / 219. 8 x 100/ 1 = 9 . 099 = 9. 2 %
The image of point (2,6) under a reflection in point T is (-16,-6). What is the image of point (18,-8) under the same DS translation? (Without graph)(-a+2x,-b+2y)
The point (2,6) is translated using the formula: (-a+2x,-b+2y). Then the final point is (-16,-6)
It means that:
if x = 2,
-a + 2x = -16
Solving for a, we get:
-a + 2(2) = -16
-a = -16 - 4
-a = -20
a = 20
At the same way, if y=6,
-b + 2y = -6
Solving for b, we get:
-b + 2(6) = -6
-b = -6 - 12
b = 18
So, the formula is (-20 + 2x, -18 + 2y)
Then, the point (18, -8) under the same translation is:
( -20 + 2(18) , -18 + 2(-8) )
( -20 + 36 , -18 - 16)
(16, -34)
write the x value for each relative maximum and relative minimum.(please label your answers as relative min or relative max)
Relative maximum is the point where the function changes direction from increasing to decreasing. Looks like a peak.
Relative minimum is the point where the function changes direction from decreasing to increasing. Looks like a valley or cusp.
Now, we can clearly see the two peaks of the function. They occur at x-values of:
[tex]x=-3,x=3[/tex]Now, the sharp turn (cusp) occurs at the y-axis, or at x = 0, which is the relative minimum.
Hence,
Rel Max occurs at x = 3 and x = -3
Rel Min occurs at x = 0
The question is in the image. Answer question 19 only.
To convert radians to degrees we need to use the following formula:
[tex]\theta\cdot\frac{180\degree}{\pi}[/tex]where θ is the angle we want to convert. In this case that angle is -5 radians, then we have:
[tex]-5\cdot\frac{180\degree}{\pi}=-286.48\degree[/tex]Therefore, -5 radian is equal to -286.48°
Drag and drop the correct number or expression into each box to complete the recursive rule to describe the sequence 8, 16, 24, 32 ... f(1) =(_____),f(n)=f(____)+______ for each whole number greater than 1. 16 n +1 8 n - 1
1) Writing a Recursive rule for that Arithmetic Sequence
Let's firstly pick the first element, a recursive rule depends on the previous element.
f(1) = 8
2) Looking at the Sequence, the common ratio is 8
f(1)= 8
f(3+1)
f(4) = 8 +(3-1)*8
f(2) = 8 +(2)8
f(2) = f(3)
For n > 1
f(2) = f(1) +8
So f(n) = f(n-1) +8
- What is the area of the giant Americanflag shown? All stripes are thesame height39 ft52 ft14 ft
We have:
Area of the American flag is:
[tex]A=\text{length}\times width[/tex]Therefore, the length is
[tex]\text{length}=39+52=91[/tex]This is, the length = 91 ft.
For the width, we have 13 stripes on the flag:
[tex]4\times13=52[/tex]The width = 52 ft
Next, the area of the giant American flag:
[tex]A=91\times52=4732[/tex]Answer: 4732 ft^2
Identify the correct trigonometry formula to use to solve for x.11Х55°
From the right-angled triangle given, let us identify the given sides with reference to the angle 55°
[tex]\begin{gathered} x\text{ is the hypotenus(the longest side opposite the right angle)} \\ 11istheadjacentsidetotheangle55^0 \end{gathered}[/tex]The correct trigonometry that has both the adjacent and the hypotenuse is the cosine
To solve for x, we will then use cosine as follows
[tex]\begin{gathered} \cos A=\frac{Adjacent}{\text{Hypotenus}} \\ \cos 55^0=\frac{11}{x} \end{gathered}[/tex][tex]undefined[/tex]