We have:
In 2010 --> 110 million
Increase in 2013 is 5% = 0.05
So, for the increase in the number of full-time workers from 2010 to 2013 is:
[tex]110\times0.05=5.5[/tex]Answer: 5.5 million
And the total amount number of full time workers in 2013 is:
[tex]110+5.5=115.5[/tex]Answer: 115.5 million
[tex]147x + (7 \times 9)[/tex]what is the answer and how to u get it
The answer is 9, letter B.
5. Triangle ADE is enlarged to form triangle ABC 6 cm 10 cm 5 cm 6 cm 7 cm 7 cm. What is the scale factor?
Notice that the length AB is 12cm, the length AC is 14cm and BC equals 10cm.
By comparing those sides with AD=6cm, AE=7cm and DE=5cm respectively, we can see that:
[tex]\begin{gathered} AB=2AD \\ AC=2AE \\ BC=2DE \end{gathered}[/tex]Therefore, the scale factor is 2.
Thea, Maria, and Pam are a teacher, a mechanic, and a pilot. None has a job that starts with the same letter as her name. Thea recently had her car repaired by the mechanic. Who has which job?
The answer is Thea - pilot, maria - teacher and pam - mechanic.
Given:
Thea, Maria, and Pam are a teacher, a mechanic, and a pilot. None has a job that starts with the same letter as her name. Thea recently had her car repaired by the mechanic.
From given statements:
Thea is not a teacher because thea name starts with t.
Maria is not a mechanic because maria name starts with m.
Pam is not a pilot because pam name starts with p.
Thea recently repaired her car by the mechanic so she is not a mechanic because if she is mechanic she can repair the car, so thea has only one possibility that she is a pilot.
Maria is not a mechanic and pilot and she has only one possibility that is she is a teacher.
Pam has only one left that is she is a mechanic.
Therefore the answer is Thea - pilot, maria - teacher and pam - mechanic.
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4+2/3x=2/5 how do I solve this equation
Given:
The given equation is 4+2/3x=2/5.
The objective is to solve for x.
[tex]undefined[/tex]I need help trying to figure out what steps to take in solving this.
To find x we need to remember the definitions of the trigonometric functions:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex][tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex][tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]Now, from the figure we notice that we know the adjacent leg to the angle given; and that we want to know the opposite leg of the same angle. Comparing what we know and what we want we conclude that we need to use the tangent function. Plugging the values into the definition of the function we have:
[tex]\tan 13=\frac{x}{8}[/tex]Solving for x we have:
[tex]\begin{gathered} \tan 13=\frac{x}{8} \\ x=8\tan 13 \\ x=1.8 \end{gathered}[/tex]Therefore x=1.8
Make a the subject of the formula:
P = square root n² + a
____
n+a
Answer:
[tex]a=\dfrac{n^2-P^2n}{P^2-1}[/tex]
Step-by-step explanation:
Given equation:
[tex]P=\sqrt{\dfrac{n^2+a}{n+a}}[/tex]
Square both sides of the equation:
[tex]\implies P^2=\dfrac{n^2+a}{n+a}[/tex]
Multiply both sides by (n + a):
[tex]\implies P^2(n+a)=n^2+a[/tex]
Expand the parentheses:
[tex]\implies P^2n+P^2a=n^2+a[/tex]
Subtract a from both sides:
[tex]\implies P^2n+P^2a-a=n^2[/tex]
Subtract P²n from both sides:
[tex]\implies P^2a-a=n^2-P^2n[/tex]
Factor out a on the left side of the equation:
[tex]\implies a(P^2-1)=n^2-P^2n[/tex]
Divide both sides by (P² - 1):
[tex]\implies a=\dfrac{n^2-P^2n}{P^2-1}[/tex]
Please help me with this question I am trying to help my son with this problem that his teacher said was not correct. Please help me break it down better for my son.Which ordered pair is the best estimate for the solution of the system of equations?y=−1/2x+4y=1/2x−3A. (7.5, 0.5)B. (7, 0.5)C. (7, 0)D. (7, 1)
Answer
The point of their intersection best estimate for the solution of the system of equations
The final answer
[tex](7,0.5)[/tex]What type of quadrilateral is formed by the points A(1, 2), B(3, 5), C(3, 8), and D(1, 5)?
Hint: Use distance formula
The type of quadrilateral is formed by the points A(1, 2), B(3, 5), C(3, 8), and D(1, 5) is parallelogram.
Given points:
A(1, 2), B(3, 5), C(3, 8), and D(1, 5)
we know that distance formula,
Distance between AB = [tex]\sqrt{(x_{2} - x_{1})^{2} +( y_{2} - y_{1})^{2} }[/tex]
= [tex]\sqrt{(3 - 1)^{2} +( 5 - 2)^{2} }[/tex]
= [tex]\sqrt{2^{2}+3^{2} }[/tex]
AB = [tex]\sqrt{13}[/tex]
BC = [tex]\sqrt{(3 - 3)^{2} +( 8 - 5)^{2} }[/tex]
= [tex]\sqrt{0^{2}+3^{2} }[/tex]
= [tex]\sqrt{9}[/tex]
= 3
BC = 3
CD = [tex]\sqrt{(1 - 3)^{2} +( 5 - 8)^{2} }[/tex]
= [tex]\sqrt{(2^{2} +3^{2} }[/tex]
CD = [tex]\sqrt{13}[/tex]
AD = [tex]\sqrt{(1 - 1)^{2} +( 5 - 2)^{2} }[/tex]
= [tex]\sqrt{0^{2}+3^{2} }[/tex]
AD = 3
AC = [tex]\sqrt{(3 - 1)^{2} +( 8- 2)^{2} }[/tex]
= [tex]\sqrt{2^{2} +6^{2} }[/tex]
AC = [tex]\sqrt{40}[/tex]
BD = [tex]\sqrt{(1 - 3)^{2} +( 5 - 5)^{2} }[/tex]
= [tex]\sqrt{2^{2} +0^{2} }[/tex]
BD = 2
Here AB = CD,BC = DA . But AC ≠ BD
Hence the pairs of opposite sides are equal but diagonal are not equal so it is a parallelogram.
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the perimeter of a rectangle can be found by using the formula P=21+2w. What is the width of the rectangle if the perimeter is 100 ft and the length is 50 ft?
Since this can't happen, let's suppose that P=150, then:
[tex]\begin{gathered} P=2l+2w \\ \Rightarrow150=2(50)+2w \\ \Rightarrow150=100+2w \end{gathered}[/tex]Now we have to move the 100 to the other side of the equation with a negative sign to get this:
[tex]\begin{gathered} 150=100+2w \\ \Rightarrow150-100=2w \\ \Rightarrow50=2w \end{gathered}[/tex]Finally, to get w, we move the 2 that's multiplying to the other side dividing the 50:
[tex]\begin{gathered} 50=2w \\ \Rightarrow\frac{50}{2}=w \\ \Rightarrow w=25 \end{gathered}[/tex]Therefore, the width of the rectangle would be 25 ft if the perimeter is 150ft, and we can see how the rectangle would look:
The table shows whether students in a class like cats and/or dogs. What percentage of students like both cats and dogs?A. 64%B. 90%C. 58%D. 65%
Total number of students that likes both dog and Cat = 194 students.
Total number of students = 335 students
Therefore,
[tex]\begin{gathered} \text{percentage = }\frac{194}{335}\times100 \\ \text{percentage}=\frac{19400}{335} \\ \text{percentage}=57.9104477612 \\ \text{percentage}\approx58percent \end{gathered}[/tex]percentage = 58%
what is 1 × 64 I need help in in 1st grafe
Always that you multiply a number by 1 you will obtain the same number
1 × 64=64
for example
1 × 5= 5
1 × 10=10
1 × 7=7
Answer:
1 x 64 = 64
Step-by-step explanation:
Anything multiplied by 1 is itself
Examples:
1 x 3 = 3
1 x 143 = 143
1 x 9849357369 = 9849357369
1 x 0 = 0
In Ms. Briscoe's class, 60% of the students have a little brother. There are 24 students in the class with little brothers. How many total students are in the class?
60% have a litle brother... it they are 24 then:
60% is to 24 as 100% is to x
so x = 24/(60%) = 24/0.6 = 40
the answer is 40
Penny is flying a kite that is at the end of 50 ft of string. The kite makes a 55° angle of depression with Penny. If the distance from the ground to Penny's hand is 4 feet, how far above the ground is the kite? Explain the solution to this problem.
Answer:
45 feet
Explanation:
We are required to find the height of the kite above the ground.
• The side opposite angle 55 degrees = x
,• The length of the hypotenuse = 50 ft
From trigonometric ratios:
[tex]\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]Therefore:
[tex]\begin{gathered} \sin 55\degree=\frac{x}{50} \\ x=50\times\sin 55 \\ x=40.96\text{ ft} \end{gathered}[/tex]Since the distance from the ground to Penny's hand is 4 feet, the height of the kite above the ground will be:
[tex]\begin{gathered} =40.96+4 \\ =44.96ft \\ \approx45ft \end{gathered}[/tex]Nelson goes to three main places most days school, work and his home. They are graphed below. What is the distance between his home and his work? 4.2 9.5 11.2 90
ANSWER
9.5
EXPLANATION
To find the distance between home and work, we have to use the formula:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]We have that home is at point (3, -3) and work is at point (0, 6).
Therefore:
(x1, y1) = (3, -3)
(x2, y2) = (0, 6)
Therefore, we have that:
[tex]\begin{gathered} D\text{ = }\sqrt[]{(0-3)^2+(6-(-3))^2} \\ D\text{ = }\sqrt[]{(-3)^2+(6+3)^2}\text{ = }\sqrt[]{(-3)^2+(9)^2} \\ D\text{ = }\sqrt[]{9\text{ + 81}}\text{ = }\sqrt[]{90} \\ D\text{ = 9.5} \end{gathered}[/tex]The answer is 9.5
19.79 and 9.08 minutes Estimate the difference in their time?
The difference between 19.79 and 9.08 is found by subtracting the two numbers.
Hence,
[tex]19.79-9.08=10.71.[/tex]The estimate of the difference is done in the following manner.
19.79 is close to 20 and 9.08 is close to 9; therefore, the easier subtraction we have to do is 20 - 9 = 11.
what is 2+2?????????
The given question is 284.7 divided by 68.3.
We can write it as:
[tex]\frac{284.7}{68.3}[/tex]Just divide it to get your answer. That is 4.1683
Answer:4
Step-by-step explanation:
Refer to the figure at the right.5. Name the intersection of DC and CB.(Example 2)6. Name all of the planes that arerepresented. (Example 3)7. Name the intersection of plane ABCand plane ACD. (Example 4)
EXPLANATION :
Note that the intersection of two lines or two segments is a point
The intersection of two planes is a line or a segment
5. Intersection of DC and CB
The intersection as shown in the figure is Point C.
So the answer is point C
6. Name all the planes that are represented.
A plane is a 2-dimensional shape. From the word itself, it can represent as a plane or a sheet.
The planes in the given figure are :
ABC, ACD, ADE, ABE, and BCDE
7. Intersection of plane ABC and plane ACD
The intersection is the common segment between the two planes.
That will be segment AC
Describe the translation of f(x) = |x|.
3 units right, 5 units up
5 units right, 3 units down
3 units right, 5 units down
5 units right, 3 units up
Answer:
(6,4), (8,4),(6,4),(8,2)
Step-by-step explanation:
I think this may be right
What’s the answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Write [tex]2[/tex] wherever you see the letter [tex]x[/tex] and you will get the result.
[tex]f(x)=-3x+5+5x-1=2x+4[/tex][tex]f(2)=2(2)+4[/tex][tex]f(2)=8[/tex]A truck driver delivers 2,000
packages every week. How many
packages does the truck driver
deliver in 7 weeks?
Answer:
14000 packages
Step-by-step explanation:
2000*7 = 14000 (packages)
Hope that this was helpful
describe the graph , and compare it to a cubic function with the same leading coefficient.
Comparing with a cubic function with the same leading coefficient, we have it that the graphs of both functions are similar as they have excatly the same end behavior summarised below;
[tex]\begin{gathered} As\text{ x}\Rightarrow+\infty\text{ , f(x)}\Rightarrow\text{ +}\infty\text{ and also;} \\ x\Rightarrow-\infty,\text{ f(x)}\Rightarrow-\infty \end{gathered}[/tex]Here, we want to make a comparism
Before we go on to make the comparism, we want to describe the graph
As can be seen from the given equation of the graph, we have a positive leading coefficenit (the coefficeint of the highest power; x^5 in this case) and an odd degree (degree refers to the highest power of the polynomial)
Using this, we can get the property of the the graph
The property is simply that;
[tex]\begin{gathered} As\text{ x}\Rightarrow+\infty\text{ , f(x)}\Rightarrow\text{ +}\infty\text{ and also;} \\ as\text{ x}\Rightarrow-\infty,\text{ f(x)}\Rightarrow-\infty \end{gathered}[/tex]Now, for a cubic function with the same leading coefficient (+1 which is positive) and the degree which is 3; both functions have the same end properties
Find the equations of the lines:with x-intercept of -2 and a slope 3.
The equation of a line with x-intercept b and slope m is given by:
[tex]y=m(x-b)[/tex]Substitute m=3 and b=-2:
[tex]\begin{gathered} y=3(x-(-2)) \\ =3(x+2) \\ =3x+6 \end{gathered}[/tex]Therefore, the equation of a line with slope 3 and x-intercept -2 is:
[tex]y=3x+6[/tex]The equation for line r can be written as y=–4/9x–2. Line s is perpendicular to line r and passes through (3,5). What is the equation of line s?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation of the line s perpendicular to line r and passes through a point ( 3 , 5) is y = [tex]\frac{9}{4}[/tex]x - [tex]\frac{47}{4}[/tex]
In the above question, it is given that
We know slope intercept form of a line = y = mx + c
The equation of a line r is = y=–4/9x–2
Comparing we get, m = [tex]\frac{-4}{9}[/tex] , c = -2
It is also given that, Line s is perpendicular to line r and passes through a point ( 3 , 5)
We know that, "If two line are perpendicular to each other and one line has slope m1 then the slope of other one is given by m1.m2 = -1"
So, we get that, slope of line s is = [tex]\frac{-4}{9}[/tex] . m = -1
m = [tex]\frac{9}{4}[/tex] and point is (3,5)
Then the equation of the line s is given by =
(y - y1) = m ( x - x1)
where x1 = 3 and y1 = 5
(y - 5) = [tex]\frac{9}{4}[/tex] (x - 3)
y = [tex]\frac{9}{4}[/tex]x - [tex]\frac{27}{4}[/tex]+ 5
y = [tex]\frac{9}{4}[/tex]x - [tex]\frac{27+ 20}{4}[/tex]
y = [tex]\frac{9}{4}[/tex]x - [tex]\frac{47}{4}[/tex]
Hence, the equation of the line s perpendicular to line r and passes through a point ( 3 , 5) is y = [tex]\frac{9}{4}[/tex]x - [tex]\frac{47}{4}[/tex]
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Answer: y=9/4x-7/4
Step-by-step explanation:
i put the other one and i got it wrong so it gave me the answer
Solve the following system of linear equations by addition. Indicate whether thegiven system of linear equations has one solution, has no solution, or has an infinitenumber of solutions. If the system has one solution, find the solution.s 4x + y = - 23| 7x + 7y = 7Answer 2 PointsKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected optiondoes not have any associated text boxes, then no further input is required.O One SolutionO No SolutionO Infinite Number of Solutions
Given:
[tex]\begin{gathered} 4x+y=-27 \\ 7x+7y=7 \end{gathered}[/tex]Find : Solution and number of solution.
Sol:.
[tex]\begin{gathered} 4x+y=-27\ldots\ldots\ldots\ldots\text{.}(1) \\ 7x+7y=7\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Subtract the equation (2) to 7 times of equation (1)
[tex]\begin{gathered} 7(4x+y)=-27\times7 \\ 28x+7y=-189 \end{gathered}[/tex][tex]\begin{gathered} eq(2)-eq(1) \\ 7x+7y-(28x-7y)=7-(-189) \\ -21x=196 \\ x=\frac{196}{-21} \\ x=-9.33 \end{gathered}[/tex][tex]\begin{gathered} 7x+7y=7 \\ 7(-9.33)+7y=7 \\ -65.33+7y=7 \\ 7y=72.33 \\ y=\frac{72.33}{7} \\ y=10.33 \end{gathered}[/tex]So here only one solution i.e. (-9.33,10.33)
help help help asap....
Answer:
6.499 is the right answer.............!
A company has made a rubber ball for $0. 02 per square foot. The company wants to spend a maximum of $1 each on a new ball.What is the diameter of the new ball to the nearest tenth of a foot?A.4. 6 feetB.2. 9 feetC.5. 8 feetD.2. 3 feet
Solution:
Solution:
How to find the diameter of the ball?
Remember that for a sphere of diameter D, the surface area is:
[tex]\begin{gathered} A=4\pi(\frac{D}{2})^2 \\ r=\frac{D}{2} \end{gathered}[/tex]In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:
[tex]\begin{gathered} 0.02\times A=1 \\ A=\frac{1}{0.02} \\ A=50 \end{gathered}[/tex]By substituting the values of A=50 in the formula below, we will have
[tex]\begin{gathered} \begin{equation*} A=4\pi(\frac{D}{2})^2 \end{equation*} \\ 50=4\times\frac{22}{7}\times(\frac{D^2}{4}) \\ 50=\frac{22D^2}{7} \\ cross\text{ multiply} \\ 50\times7=22D^2 \\ 22D^2=350 \\ \frac{22D^2}{22}=\frac{350}{22} \\ D^2=\frac{350}{22} \\ D=\sqrt{\frac{350}{22}} \\ D=4.0feet \end{gathered}[/tex]Hence,
Since the company wants to spend a maximum $1,
The diameter of the new rubber ball, to the nearest foot, must be D = 4.0 ft (in the case of the maximum cost).
Hence,
From my act prep guide I need this practice problem answeredcalc subject
The standard form of the equation of a circle with centre (a,b) and radius r, is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]From the question, we provided with the following;
[tex]\begin{gathered} \text{diameter}=8\text{units} \\ \text{ Recall that:} \\ \text{Radius}=\frac{diameter}{2} \\ R=\frac{8}{2}=4\text{units} \\ \\ \text{Centre (a,b)=(2,-4)} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} (x-2)^2+(y-(-4))^2=4^2 \\ (x-2)^2+(y+4)^2=16 \end{gathered}[/tex]Hence, the equation of the circle is:
[tex](x-2)^2+(y+4)^2=16[/tex]For a line on a coordinate plane line with point A at (1,10) and point B at (7,4): 8) What is the midpoint of the line? For a line on a coordinate plane line with point A at (7,10) and point B at (4,6): 9) How long is the line? List the four types of angles based on the size of the angle: 10) 11) 12) 13) List two types of angle pairs: 14) 15)
8) or a line on a coordinate plane line with point A at (1,10) and point B at (7,4): What is the midpoint of the line?
A = (X1,Y1 )= (1,10)
B= (X2,Y2)= (7,4)
To find the midpoint we have to add each coordinate and divide it by 2:
midpoint x = (x1+x2)/2 = (1+7) /2 = 8/2 =4
Midpoint y= (y1+y2)/2 = (10+4)/2 = 14/2 = 7
So , the midpoint of the line is (4,7)
Find the greatest common factor of 18 ,12 and 42 .
The Factors of the numbers are as follows;
[tex]\begin{gathered} 18=2\times3\times3 \\ 12=2\times2\times3 \\ 42=2\times3\times7 \end{gathered}[/tex]The common factors are 2 and 3.
Therefore, the Greatest Common Factor is (2 x 3) 6
Leo buys a new car for $17,600. The simple interest rate is 8.4% and the amount of loan (plus simple interest) is repayable in 5 years. What is the total amount that must be repaid?
Solution:
Given;
[tex]P=17,600,r=8.4\text{ \%,}=0.084,t=5[/tex]The simple interest, I, is;
[tex]\begin{gathered} I=17600\times0.084\times5 \\ \\ I=7392 \end{gathered}[/tex]Thus, the amount to be repaid is;
[tex]\begin{gathered} A=P+I \\ \\ A=17600+7392 \\ \\ A=24992 \end{gathered}[/tex]The amount that must be repaid is $24,992