Orang has worked as a nurse at Springfield general hospital for 5 years longer than her friend Bill. Two years ago she had been at the hospital for twice as long. How long has each been at the hospital?
Answers
Answer:
• Bill = 3 years
,• Hoang = 8 years.
Explanation:
Let the time Bill had worked in the hospital = b years.
Hoang has worked for 5 years longer than her friend Bill, therefore:
• The time ,Hoang, had worked in the hospital = (b+5) years.
Two years ago:
• Bill's Time = (b-2) years
,• Hoang's Time = (b+5-2) years
Two years ago she had been at the hospital for twice as long as Bill.
[tex]\implies b+5-2=2b[/tex]Solve the equation for b:
[tex]\begin{gathered} b+5-2=2b \\ b+3=2b \\ 2b-b=3 \\ b=3 \end{gathered}[/tex]Hoang has been at the hospital for 8 years and Bill has been there 3 years.
Related Questions
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
Answers
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
In this problem
Applying proportion
we have
4/10=x/28
solve for x
x=(4/10)*28
x=11.2
therefore
answer is 11 booksA boat is heading towards a lighthouse, whose beacon-light is 135 feet above the water. The boat's crew measures the angle of elevation to the beacon, 4 deg What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary .
Answers
The ship's horizontal distance from the lighthouse is: 1930.59 feet.
What is tangent or tan in trigonometry?
The ratio of the side opposite the angle we know or want to know over the side next to that angle is known as the tangent, which is sometimes abbreviated as T-A-N. The side touching the angle that is NOT the hypotenuse, or the side opposite the right angle, is the neighboring side.
Given in the question,
Height of lighthouse = 135 feet,
angle of elevation = 4 degree,
We know that, tan Θ = perpendicular/ base
Here, height is perpendicular and distance is base,
Putting the values,
tan4° = 135/B
B = 1930.59 feet
Therefore, distance is 1930.59 feet.
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Answer:The answer is 1930.59
Step-by-step explanation:
What is the probability that the spinner lands on blue?
Answers
Answer:
Concept:
The total number of angles in a circle is
[tex]\begin{gathered} =360^0 \\ =120^0+60^0+180^0=360^0 \end{gathered}[/tex]The angle of the sector that represents blue is
[tex]=60^0[/tex]To calculate the probability, we will use the formula below
[tex]\begin{gathered} P(\text{blue)}=\frac{n(\text{blue)}}{n(S)} \\ n(\text{blue)}=60^0,n(S)=360^0 \\ P(\text{blue)}=\frac{n(\text{blue)}}{n(S)}=\frac{60}{360} \\ P(\text{blue)}=\frac{1}{6} \end{gathered}[/tex]Hence,
The final answer is = 1/6
1. Find the area of the triangle below. 13 in9in7in18 in63 inches squared91 inches squared126 inches squaredO 45.5 inches squared
Answers
ANSWER:
63 square inches
STEP-BY-STEP EXPLANATION:
We have the formula to calculate the area of the triangle is the following:
[tex]A=\frac{b\cdot h}{2}[/tex]Replacing:
[tex]\begin{gathered} A=\frac{7\cdot18}{2} \\ A=63 \end{gathered}[/tex]The area equals 63 square inches
To construct a square, match the corresponding steps to the proper orders. (basically match the words on the left with the number of steps 1-6)
Answers
Given:
Construct a square by matching the corresponding steps to the proper orders.
Explanation:
a) The first step would be,
Draw a line segment AB.
Therefore, statement 1 itself is the first step.
b) The second step would be,
Construct a perpendicular line to AB at B.
Therefore, statement 2 itself is the second step.
c) The third step would be,
Measure the distance AB with the compass. Draw an arc on the perpendicular line from B.
Therefore, statement 3 itself is the third step.
d) The fourth step would be,
Label it as C. Draw an arc from C without changing the measurements.
Therefore, statement 4 itself is the fourth step.
e) The fifth step would be,
Place the compass at A. Draw an arc from A without changing the measurements to intersect the previous arc.
Mark it as D.
Therefore, statement 5 itself is the fifth step.
f) The sixth step would be,
Connect ABCD.
Therefore, statement 6 itself is a sixth step.
hunter says that there should be a decimal point in the quotient below after 6. is he correct? use number sense to explain your answer. 69.48 ÷ 7.2= 965
Answers
Solution
For this case we can do this:
[tex]undefined[/tex]Question 2 Find the area of the figure below. Ty below. 24 yd 24 yd 24 yd 40 yd
Answers
Answer:
1536 yd²
Explanation:
To find the area of the figure, we need to divide the figure into 2 rectangles as:
So, the area of the first rectangle is equal to:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 24 yd x 24 yd} \\ \text{Area = 576 yd}^2 \end{gathered}[/tex]In the same way, the area of the second rectangle is:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 40 yd }\times24\text{ yd} \\ \text{Area = 960 yd}^2 \end{gathered}[/tex]So, the area of the figure is:
576 yd² + 960 yd² = 1536 yd²
Therefore, the answer is 1536 yd²
a triangle has side lengths for 8 in and 7 in select all the possible lengths for the third side 6 inches 15 inches 7 inches 20 inches 9 inches
Answers
To answer this question, we need to take into account the triangular inequality, that is, in a triangle, the sum of two sides must be greater than one side of the triangle. That is:
[tex]a+b>c,b+c>a,a+c>b[/tex]We can see that two of the sides are:
a = 8 in, and b = 7 in, then, we have:
a + b = 8 + 7 = 15. Therefore:
[tex]15>6,\text{ and 15>7,15>9}[/tex]Therefore, the possible lengths for the third side are:
• 6 inches
,• 7 inches
,• 9 inches
A sandwich shop has 70 stores and 90% of the stores are in California. The rest of the stores are in Nevada. How many stores are in California and how many are in Nevada?There are ____ stores in California and ____ in Nevada.
Answers
The sandwich shop has a total of 70 stores, this is the 100% of their stores.
90% of the stores are in California
The rest of the stores, 10%, are in Nevada.
To calculate how many stores correspond to the 90% you can use cross multiplication
100%_____70 shops
90%______x shops
[tex]\begin{gathered} \frac{70}{100}=\frac{x}{90} \\ x=(\frac{70}{100})90 \\ x=63 \end{gathered}[/tex]So the 90% of 70 is 63, this means that there are 63 stores in California.
Now subtract the number of stores in California from the total number of stores
[tex]70-63=7[/tex]And we get that there are 7 stores in Nevada
What is the equation of the line passing through the points( 29 ) and 2) in slope-intercept form?O y-zx-3O y-3x+o y = 2 x - 22O x- x+Mark this and retumSave and ExitNexSubmit
Answers
The slope-intercept form is
[tex]y=mx+b[/tex]First we find m which is defined as rise / run
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{y_1-y_2}{x_1-x_2}[/tex][tex]\Rightarrow m=\frac{(\frac{11}{12})-(\frac{19}{20})}{(\frac{1}{3})-(\frac{2}{5})}[/tex][tex]m=\frac{1}{2}[/tex]And finally, we find the y-intercept b from one of the points given.
Let us use the point (1/3, 11/12).
[tex]\frac{11}{12}=\frac{1}{2}(\frac{1}{3})+b[/tex][tex]\frac{11}{12}=\frac{1}{6}+b[/tex][tex]b=\frac{11}{12}-\frac{1}{6}[/tex][tex]b=\frac{3}{4}[/tex]Hence, the equation of the line in slope-intercept form is
[tex]y=\frac{1}{2}x+\frac{3}{4}[/tex]which is the second choice in the column.
If you shift the function F(x) = log10 x right three units, what is the newfunction, G(x)?O A. G(x) = log, (x-3)O B. G(x) = log, (x+3)O C. G(x) = 109, *-3O D. G(x) = 109,X+3
Answers
Given the function:
[tex]F\mleft(x\mright)=log_{10}x[/tex]You need to remember that, according to the Transformation Rules for Functions:
1. If:
[tex]f(x+h)[/tex]The function is shifted left "h" units.
2. If:
[tex]f(x-h)[/tex]The function is shifted right "h" units.
In this case, you know that F(X) is shifted right three units to obtain the new function G(x), then the transformation has this form:
[tex]F(x-3)[/tex]Therefore, you can determine that:
[tex]G(x)=\log _{10}\mleft(x-3\mright)[/tex]Hence, the answer is: Option A.
11.) SOLVE the equation for w by using "factoring by grouping". YOUMUST SHOW ALL STEPS of the grouping process, especially theFIRST STEP of grouping to receive FULL CREDIT. (10 pts)2w3 + 5w2 - 32w - 80 = 0
Answers
ANSWER:
w = -5/2, w = 4 and w = -4
STEP-BY-STEP EXPLANATION:
We have the following equiation:
[tex]2w^3+5w^2-32w-80=0[/tex]We solve with the help of factoring by grouping
[tex]\begin{gathered} (2w^3+5w^2)+(-32w-80)=0 \\ w^2\cdot(2w+5)-16\cdot(2w+5)=0 \\ (2w+5)\cdot(w^2-16)=0 \\ 2w+5=0\rightarrow w=-\frac{5}{2} \\ (w^2-16)=0\rightarrow w^2=16\rightarrow w=\pm4\rightarrow w=4,w=-4 \end{gathered}[/tex]The solutions are w = -5/2, w = 4 and w = -4
Explain how I know the vertex of m(x)=x(x+6)
Answers
Answer: a lot of 5
Step-by-step explanation:
yes
Answer:
Rewrite in vertex form and use this form to find the vertex (h,k)(h,k).(12,−254)
Step-by-step explanation:
Hope this helps ;)
If P(6,-2). O(-2,8), R(-4, 3), and S(-9, y). find the value of y so that PO perpendicular to RS.please?
Answers
Answer:
y = - 1
Explanation:
Two lines are perpendicular if the product of their slopes is equal to -1.
Additionally, we can calculate the slope of a line with two points (x1, y1) and (x2, y2) as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace (x1, y1) by P(6, -2) and (x2, y2) by O(-2, 8), we get that the slope of PO is equal to:
[tex]m=\frac{8-(-2)}{-2-6}=\frac{8+2}{-8}=\frac{10}{-8}=-1.25[/tex]In the same way, if we replace (x1, y1) by (-4, 3) and (x2, y2) by (-9, y), we get that the slope of RS is equal to:
[tex]m_{}=\frac{y-3}{-9-(-4)}=\frac{y-3}{-9+4}=\frac{y-3}{-5}[/tex]Then, the product of these two slopes should be equal to -1, so we can write the following equation:
[tex]-1.25\cdot(\frac{y-3}{-5})=-1[/tex]So, solving for y, we get:
[tex]\begin{gathered} (-5)(-1.25)\cdot(\frac{y-3}{-5})=(-5)(-1) \\ -1.25(y-3)=5 \\ y-3=\frac{5}{-1.25} \\ y-3=-4 \\ y=-4+3 \\ y=-1 \end{gathered}[/tex]Therefore, the value of y is equal to -1
for a function f(x)=x^2, write an equation for that function stretched vertically by a factor of 4, and shifted 2 units to the right
Answers
the initial function is:
[tex]f(x)=x^2[/tex]to stretch the fuction vertically we have to divide by 4 y so:
[tex]\begin{gathered} \frac{f(x)}{4}=x^2 \\ f(x)=4x^2 \end{gathered}[/tex]now to move two units to the right we have to rest 2 in the x so:
[tex]f(x)=4(x-2)^2[/tex]A van with seven people drove 422 miles six hours. About how many miles did they travel each hour?
Answers
Distance travelled by van in six hours is 422 miles.
Determine the distance travelled by the van in one hour.
[tex]\begin{gathered} \frac{422}{6}=70.333 \\ \approx70.3\text{ miles} \end{gathered}[/tex]So, they travel approximately 70.3 miles in each hour.
Which of the following represents vector vector u equals vector RS in linear form, where R (–22, 6) and S (–35, 14)?
Answers
Given two points R(xR, yR) and S(xS, yS), the vector v = RS is found as follows:
[tex]v=[/tex]In this case, the points are R (–22, 6) and S (–35, 14), then the vector is:
[tex]\begin{gathered} v=<-35-(-22),14-6> \\ v=<-13,8> \\ Or \\ v=-13i+8j \end{gathered}[/tex]What is the worst part of being a girl?
Answers
Answer:
men.
Step-by-step explanation:
just men
Answer:
is this really a question?...
Step-by-step explanation:
Kirby wants to run a total of 7 5/8 miles every Tuesday and Thursday. If he runs 4 4/16 miles onTuesday and 3 3/8 miles on Thursday, will he meet his goal for this week? Explain.
Answers
Given:
Kirby wants to run a total of 7 5/8 miles every Tuesday and Thursday.
If he runs 4 4/16 miles on Tuesday and 3 3/8 miles on Thursday,
Then, the total miles he will cover is,
[tex]\begin{gathered} 4\frac{4}{16}+3\frac{3}{8}=4\frac{1}{4}+3\frac{3}{8} \\ =\frac{17}{4}+\frac{27}{8} \\ =\frac{34}{8}+\frac{27}{8} \\ =\frac{61}{8} \\ =7\frac{5}{8} \end{gathered}[/tex]Since, he will cover total of 7 5/8 miles.
So, he will meet his goal for this week.
We estimate that the population of a certain, in t years will be given byp (t) = (2t² + 75) / (2t² + 150) million habitantsAccording to this hypothesis:What is the current population?What will it be in the long term?Sketch the population graph
Answers
Given that the population can be represented by the equation;
[tex]P(t)=\frac{2t^2+75}{2t^2+150}[/tex]The current population (Initial population) is the population at time t=0;
Substituting;
[tex]t=0[/tex][tex]\begin{gathered} P(0)=\frac{2t^2+75}{2t^2+150}=\frac{2(0)^2+75}{2(0)^2+150}=\frac{75}{150} \\ P(0)=0.5\text{ million} \end{gathered}[/tex]Therefore, the current population of the habitat is;
[tex]0.5\text{ million}[/tex]The long term population would be the population as t tends to infinity;
[tex]\begin{gathered} \lim _{t\to\infty}P(t)=\frac{2t^2+75}{2t^2+150}=\frac{2(\infty)^2+75}{2(\infty)^2+150}=\frac{\infty}{\infty} \\ \lim _{t\to\infty}P(t)=\frac{4t}{4t}=1 \end{gathered}[/tex]Therefore, the long term population of the habitat is;
[tex]P(\infty)=1\text{ million}[/tex]which values are in the domain of the function F(X)= -6x + 11 with a range of (-37 ,-25, -13, -1)? select all that apply a)1b)4c)8d)5e)2f)6g)3h)7
Answers
Answers:
2
4
6
8
Explanation:
The domain of the function with a range {-37, -25, -13, -1} will be the set of values of x when f(x) is -37, -25, -13, and -1. So, to find the correct answers, we need to solve the following equations:
If f(x) = -37, we get:
[tex]\begin{gathered} f(x)=-6x+11 \\ -37=-6x+11 \\ -37-11=-6x+11-11 \\ -48=-6x \\ \frac{-48}{-6}=\frac{-6x}{-6} \\ 8=x \end{gathered}[/tex]If f(x) = - 25, we get:
[tex]\begin{gathered} -25=-6x+11 \\ -25-11=-6x+11-11 \\ -36=-6x \\ \frac{-36}{-6}=\frac{-6x}{-6} \\ 6=x \end{gathered}[/tex]If f(x) = - 13, we get:
[tex]\begin{gathered} -13=-6x+11 \\ -13-11=-6x+11-11 \\ -24=-6x \\ \frac{-24}{-6}=\frac{-6x}{-6} \\ 4=x \end{gathered}[/tex]If f(x) = -1, we get:
[tex]\begin{gathered} -1=-6x+11 \\ -1-11=-6x+11-11 \\ -12=-6x \\ \frac{-12}{-6}=\frac{-6x}{-6} \\ 2=x \end{gathered}[/tex]Therefore, the domain is the set of the values of x: {2, 4, 6, 8}
Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.(2, -1)
Answers
In polar coordinates we must have two things to plot a point, it's the radius and the angle
If we use a negative angle, it just means that we are doing the rotation clockwise.
Therefore the point (2, -π) is
We do a 2 units long line and rotate is by -π, the result is
Determine whether each number is a solution of the given inequality.5b - 7>13
Answers
Solve for b:
Add 7 to both sides:
[tex]\begin{gathered} 5b-7+7>13+7 \\ 5b>20 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5b}{5}>\frac{20}{5} \\ b>4 \end{gathered}[/tex]Answer:
b > 4
which of the following Roots would be between 8 and 7
Answers
To find which of the following roots is between "8" and "7" we can calculate the root of which numbers result in 8 and 7. To do this we will power them by 2, this is done because power is the oposite operation to the root. Doing this gives us:
[tex]\begin{gathered} 8^2=64 \\ 7^2=49 \end{gathered}[/tex]So the root of 64 is 8 and the root of 49 is 7. We need to find the number that is between 49 and 64.
From the options the only one that qualifies is 52. The correct option is b.
Find the z-scores for which 70% of the distribution's area lies between - Z and z.
Answers
The values given by z-score tables represent the fraction of the area under a normal curve between -∞ and z. For example, for a given z, the value given by a table represents the following area:
However, in this exercise we must find the area under the curve between -z and z and not between -∞ and z. We are basically looking for an area like this one:
So the z in a z-score table that corresponds to 70% of the area is not the answer.
However, we still can find the value of z using a z-score table. Remember that the total area under this curve is equal to 1. We are told that the area between -z and z is the 70% so this area is equal to 0.7. Then the remaining area i.e. the sum of the areas at the left of -z and at the right of z is equal to 1-0.7=0.3. Another important property of the normal distribution curve is that it's symmetric so the area at the right of z is equal to that at the left of -z then the two green areas are equal and their sum is 0.3. This means that each green area is equal to 0.3/2=0.15. So basically we have the following:
- The area between -∞ and -z is equal to 0.15.
- The area between z and ∞ is equal to 0.15.
Remember that the z-scores tables give us the z-score associated with the area under the curve between -∞ and z. Then if we look at a z-score table and look for the value 0.15 the table will give us the value of -z and with it the value of z. So we must look for 0.15 in a z-score table:
0.14917 is the closest value to 0.15 in this table so it is useful. As you can see it's located at row -1 and column 0.04 which means that it corresponds to -1.04. Then -z=-1.04 and therefore z=1.04. Then the answer is:
[tex]-1.04,1.04[/tex]Choose the expression that is equivalent to 9w² +3/5(20w² - 15w+10)+2w
Answers
The correct answer or equivalent expression is 21w² - 7w + 6.
What is the equivalent of an expression?X-terms and constants should be combined with any other like and similar terms on either side of the equation. By putting the terms in the same order, with the x-term usually comes before the constants. The two phrases or equation are equal if and only if each of their terms is the same.
It is given in the question that 9w² +[tex]\frac{3}{5}[/tex](20w² - 15w+10)+2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] (20w² - 15w+10)+ 2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] × 5 (4w² - 3w+2) + 2w
⇒ 9w² + 3(4w² - 3w+2) + 2w
⇒ 9w² + 12w² - 9w + 6 + 2w
⇒ 21w² - 7w + 6
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Jaron made a trip of 450 miles in 8hours. Before noon he averaged 60 miles per hour , and afternoon he averaged 50 miles per hour. At what time did he begin his trip and when did he end it?
Answers
Data:
Total distance: 450 miles
Total time: 8 h
Average 60 mi/h before noon
Average 50 mi/h afternoon
The relationship between the time, speed (average) and distance is drescribed in the next equations:
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ d=s\times t \\ \\ \end{gathered}[/tex]Then, if you multiply the speed and the time you get the distance:
time before noon: b
time afternoon: a
[tex](60\times b)+(50\times a)=450[/tex]The sum of a and b is the total time:
[tex]a+b=8[/tex]Use the next system of equations to find a and b:
[tex]\begin{gathered} 60b+50a=450 \\ a+b=8 \end{gathered}[/tex]1. Solve a in the second equation:
[tex]\begin{gathered} \text{Subtract b in both sides of the equation:} \\ a+b-b=8-b \\ \\ a=8-b \end{gathered}[/tex]2. Substitute the a in first equation by the value you get in first step:
[tex]60b+50(8-b)=450[/tex]3. Solve b:
[tex]\begin{gathered} 60b+400-50b=450 \\ 10b+400=450 \\ \\ \text{Subtract 400 in both sides of the equation:} \\ 10b+400-400=450-400 \\ 10b=50 \\ \\ \text{Divide both sides of the equation into 10:} \\ \frac{10}{10}b=\frac{50}{10} \\ \\ b=5 \end{gathered}[/tex]4. Use the value of b=5 to solve a:
[tex]\begin{gathered} a=8-b \\ a=8-5 \\ a=3 \end{gathered}[/tex]Then, Jaron begin his trip 5 hours before noon ( at 7:00) and end it 3 hours afternoon (at 15:00)Consider the following set of equations:Equation M: 3y = 3x + 6Equation P: y = x + 2Which of the following best describes the solution to the given set of equations? No solutionOne solutionTwo solutionsInfinite solutions
Answers
Solution
Given
Equation M: 3y = 3x + 6
Equation P: y = x + 2
Plot the graph of the two equation
The graph of the two equations are the same. With the same slope and intercept
The graph is shown below
Conclusion:
Because the graph of the equatons are thesame, the system of equations have Infinite solutions
The answer is Infinite solutions
3x – 2y= 12Find the x- and y-intercepts from the equation in standard form above. Explain how you got each intercept.
Answers
To find the y-intercept, we have to make x=0 and solve for y:
[tex]\begin{gathered} 3x-2y=12 \\ x=0 \\ \Rightarrow3\cdot0-2y=12 \\ \Rightarrow-2y=12 \\ \Rightarrow y=\frac{12}{-2}=-6 \\ y=-6 \end{gathered}[/tex]Now, to find the x-intercept, we make y=0 and do the same as the previous case:
[tex]\begin{gathered} y=0 \\ \Rightarrow3x-2\cdot0=12 \\ \Rightarrow3x=12 \\ \Rightarrow x=\frac{12}{3}=4 \\ x=4 \end{gathered}[/tex]therefore, the y-intercept is the point (0,-6) and the x-intercept is the point (4,0)
Window45°Apartment450BenchNoah can see a bench in the nearby play area through his window inhis apartment at a 45° angle of depression.If the floor of the apartment that Noah is standing is 25 feet abovethe ground level, what is the horizontal distance from the apartmentto the bench in the play area?
Answers
Given:
The angle of depression of the bench with respect to Noah, θ=45° .
The height of the apartment or the height at which Noah is standing with respect to the ground, h=25 feet.
Let x be the horizontal distance from the apartment to the bench.
Now, using trigonometric property in the above triangle,
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan \theta=\frac{h}{x} \end{gathered}[/tex]Substitute the values and solve the equation for x.
[tex]\begin{gathered} \tan 45^{\circ}=\frac{25\text{ ft}}{x} \\ 1=\frac{25\text{ ft}}{x} \\ x=25\text{ ft} \end{gathered}[/tex]Therefore, the horizontal distance from the apartment to the bench is 25 ft.