State A have 42 counties and State B have 40 counties.
Define Linear equation
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant
Let,
x = The number of counties of state B
x + 2 = The number of counties of State A
It's given, The sum of counties of state A and state B is 82
so, the equation become is linear.
The linear equation will be,
x + (x + 2) = 82
solve for x,
2x + 2 = 82
2x = 82 - 2
2x = 80
x = 80/2
x = 40 (counties of State B)
put the value in x in x + 2,
40 + 2 = 42 (counties of State A)
Therefore, State A have 42 counties and State B have 40 counties.
To read more about the Linear equation
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Chase and his brother want to improve their personal information for when they startapplying to colleges of their choice. To accomplish this they decide to help the SalvationArmy with delivering hot meals to senior citizens. About a month ago, they decided tokeep track of how many successful deliveries they have each completed. As of today,Chase has successfully delivered 18 out of the 30 meals to senior citizens.Part AHow many more meals would Chase have to deliver in a row in order to have a 75%successful delivery record? Justify your answer.Part BHow many more meals would Chase have to deliver in a row in order to have a 90%successful delivery record? Justify your answer.PartAfter successfully delivering 18 out of 30 meals would Chase ever be able to reach a100% successful delivery record? Explain why or why not.
Part A.
Chase has successfully delivered 18 out of the 30 meals to senior citizens.
We have to calculate how many more meals (lets call it x) she has to deliver to have a 75% successful delivery record.
In order to do that, (18+x) meals have te be delivered successfully out of (30+x), and the successful meals (18+x) divided by (30+x) has to be 0.75:
[tex]\begin{gathered} \frac{18+x}{30+x}=0.75 \\ 18+x=0.75(30+x) \\ 18+x=22.5+0.75x \\ x-0.75x=22.5-18 \\ 0.25x=4.5 \\ x=\frac{4.5}{0.25} \\ x=18 \end{gathered}[/tex]Chase has to deliver 18 more meals successfully in order to have a 75% success delivery record.
Part B.
We apply the same analysis but we replace 0.75 with 0.9 as the delivery record.
[tex]\begin{gathered} \frac{18+x}{30+x}=0.9 \\ 18+x=0.9(30+x) \\ 18+x=27+0.9x \\ (1-0.9)x=27-18 \\ 0.1x=9 \\ x=\frac{9}{0.1} \\ x=90 \end{gathered}[/tex]Chase has to deliver 90 more meals successfully in order to have a 90% success delivery record.
Part C.
She won't be able to achieve 100% successful delivery record. We can prove it mathematically, but we already know as there are 12 meals that weren't successfully delivered, so we can get close to 100% but it can't never be reached.
Mathematically we have:
[tex]\begin{gathered} \frac{18+x}{30+x}=1 \\ 18+x=30+x \\ x-x=30-18 \\ 0=12 \end{gathered}[/tex]This solution is not valid, so there is no valid solution for x.
What happens to F(x) when x is negative but approaches zero for the functionF(x) = 1/x, whose graph is shown below?
Given: The graph of the function below
[tex]F(x)=\frac{1}{x}[/tex]To Determine: What happens to F(x) when x is negative but approaches zero
Solution:
It can be observed from the given graph that when x is negative but approaches zero, F(x) approaches negative infinity
This is as shown below
From the options provided, the best answer is F(x) is a negative number, OPTION C
7(x+2)=
4(x+4)=
9(x+6)=
Which statement about the graph below is true?
Answer:
a. The relation is a function because every input has an output.
Step-by-step explanation:
a relation in which for every input there is exactly one output (for every x there is just one y)
quizlet
Answer:
A. The relation is a function because every input has an input
Step-by-step explanation:
A relation is a function as long as there are not multiple outputs for one input. It's okay if there are multiple inputs for one output, like we can see here with points (-6, 1) and (2, 1).
Another way to test if a graphed relation is a function is the vertical line test. Draw vertical lines at multiple spots on the graph and if any of the vertical lines touches 2 points, the graphed relation is not a function.
:)
Options for this are: 20 of the best selling cameras, same photographer, 100 pictures with each camera, consistent across all cameras 10 point scale, two were from companies who are major advertisers
It is given that:
A writer for a magazine recently did a test to determine which mid-range digital camera takes the best pictures. Her method is described below.
Which part of the method describes an area of potential bias?
She gathered 20 of the best.selling cameras and used the same photographer to take 100 pictures with each camera .She ensured that the environment and the subject of each picture were consistent across all cameras and used a 10.point scale to determine picture quality. Of the cameras tested, two were from companies who are major advertisers in the magazine.
Now if the reading is done carefully, it can be concluded that the information given by:
"Of the cameras tested, two were from companies who are major advertisers in the magazine." can be considered for a potential bias since the magazine may be pressured by these two companies to give them a higher rating than they deserve.
So the option:two were from companies who are major advertisers is correct.
Slove this equation 19=n+22
Step-by-step explanation:
I think it helps you
please mark me as brainlist
Answer:
greyehahhsh[tex]5.5723[/tex]Is my answer correct help please
Answer:
Yes your answer is right !
Step-by-step explanation:
steps
X= 3 and y = 7
So first replace [tex]2^{x}[/tex] with [tex]2^{3}[/tex] an that will give you 8Then 8-Y and so you replace y with 7 and so it becomes
8-7 = 1So the correct answer is D (1)
Hope this helps
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hailey is going to rent an apartment for $864 a month in addition to the first month's rent when moving in a security deposit of $216 is required what will be the total payments required when moving in
We are given that a total amount is $864, if a deposit of $216 is given, then the total amount to pay is the following:
[tex]864-216=648[/tex]Therefore, there is $648 to pay.
What is the divisibility rule for 4
A. Last two digits divisible by 4
B. Add all of the digits and divide by 4
C. Last 3 digits divisible by 4
D. Even number
Answer :- A) Last two digits divisible by 4.
Suppose you are in a restaurant and the menu is as follows: 5 beverages, 11 appetizers, 9 main courses, and 3 desserts. Impose the condition that exactly one choice must be made from each category. How many
distinguishable meals can be created?
Answer:
1485
Step-by-step explanation:
The answer is found by multiplying how many of each of the categories there are;
5 × 11 × 9 × 3 = 1485
Select all the correct locations on the image.Which statements are logically equivalent to (p q)?
-(p ∧ q ) is logically equivalent to
-pv-q
With the information given, find the lenght of the prism
Answer:
The lenght of the prism is 22 cm.
Step-by-step explanation:
From the given drawing, we can conclude that a one-unit line measures 2 cm. Since the prism is 11 unit lines long, we can conclude that it is 22 cm.
Need help finding the volume and rounding to nearest whole number.
For a cylinder, the volume can be calculated using the formula:
[tex]V=\pi r^2h[/tex]Where r is the radius of the base and h is the height. From the problem, we identify:
[tex]\begin{gathered} r=\frac{16}{2}=8\text{ yd} \\ \\ h=10\text{ yd} \end{gathered}[/tex]Then, using these values to calculate the volume of the cylinder:
[tex]\begin{gathered} V=\pi(8)^2(10)=\pi(64)(10)=640\pi \\ \\ \therefore V=2011\text{ yd}^3 \end{gathered}[/tex]Find all x-intercepts of the following function. Write your answer or answers as
coordinate points. Be sure to select the appropriate number of x-intercepts.
f(x)
3x + 30
25x2 - 49
Given: The function below
[tex]f(x)=\frac{3x+30}{25x^2-49}[/tex]To determine: All x-intercepts of the given function
The x-intercept is a point where the graph crosses the x-axis
We would substitute the function equal to zero and find the value of x
[tex]\begin{gathered} f(x)=\frac{3x+30}{25x^2-49},f(x)=0 \\ \text{Therefore} \\ \frac{3x+30}{25x^2-49}=0 \\ \text{cross}-\text{ multiply} \\ 3x+30=0 \end{gathered}[/tex][tex]\begin{gathered} 3x=-30 \\ \frac{3x}{3}=\frac{-30}{3} \\ x=-10 \end{gathered}[/tex]Therefore, the coordinate of the x-intercept is (-10, 0)
Solve the following addition and subtraction problems.3 km9hm9dam19 m+7km2 dam5sq km95 ha8,994sq m+11sq km11 ha9,010sq m44m−5dm72km47hm2dam−11 km55hm
As a well accepted rule to solve this problem, we would transform all values to the lower units.
so for the first question:
3 km 9hm 9 dam 19 m + 7 km 2 dam
3,000 m 900 m 90 m 19 m + 7,000 m 20 m
= 4,009 + 7,020
= 11,029 m
The second question:
5 sq.km 95 ha 8,994 sq.m + 11 sq.km 11 ha 9,010 sq.m
5,000,000 sq m 95,0000 sq m 8,994 sq m + 11,000,000 sq m 110,000 sq 9,010 sq m
= 5,103,994 sq m + 11,119,010 sq m
= 16,223,004 sq m
The third question:
44 m - 5 dm
44 m - 0.5 dm
= 43.5 m
The fourth question:
72 km 47 hm 2 dam - 11 km 55 hm
72,000 m 4,700 m 20 m - 11,000 m 5,500 m
= 76,720 m - 16, 500 m
= 60,220 m
Rearrange the formula y = a-bx² to make x the subject.
Answer:
x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]
Step-by-step explanation:
y = a - bx² ( subtract a from both sides )
y - a = - bx² ( multiply through by - 1 )
bx² = a - y ( divide both sides by b )
x² = [tex]\frac{a-y}{b}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{a-y}{b} }[/tex]
Solve by applying the zero product property.m^2= 27-6m
To apply the zero product property we first need to write all the terms of the equation on side:
[tex]\begin{gathered} m^2=27-6m \\ m^2+6m-27=0 \end{gathered}[/tex]Now we need to factorise the expression on the right:
[tex]\begin{gathered} m^2+6m-27=0 \\ (m+9)(m-3)=0 \end{gathered}[/tex]The last line indicates that the product of two numbers is equal to zero this means that one of them has to be zero (this is the zero product property), then we have:
[tex]\begin{gathered} m+9=0 \\ m=-9 \\ or \\ m-3=0 \\ m=3 \end{gathered}[/tex]Therefore, the solutions of the equation are m=-9 and m=3
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
option 3
Step-by-step explanation:
As long as both lines are rotated the same direction and the same angle, then the angle between the two lines will not change.
The perimeter of the triangle below is 91 units. Find the length of the side QR. write your answer without variables.
Given:
The perimeter of the triangle, P=91.
The sides of the triangle are,
PR=4z
QR=z+3
PQ=5z-2.
The perimeter of the triangle can be expressed as,
[tex]\begin{gathered} P=PR+QR+PQ \\ P=4z+z+3+5z-2 \\ P=10z+1 \end{gathered}[/tex]Now, put P=91 in the above equation to find the value of z.
[tex]\begin{gathered} 91=10z+1 \\ 91-1=10z \\ 90=10z \\ \frac{90}{10}=z \\ 9=z \end{gathered}[/tex]Now, the length of the side QR can be calculated as,
[tex]\begin{gathered} QR=z+3 \\ QR=9+3 \\ QR=12 \end{gathered}[/tex]Now, the length of QR is 12 units.
What is the equation of the line below in slope-intercept form?(4 Points)x-3y = 6y =- 2y = 3x - 2y = - ** - 2y = -3x - 2
Let's make y the subject of the equation.
[tex]\begin{gathered} x-6=3y \\ y=\frac{x-6}{3} \\ y=\frac{1}{3}x-\frac{6}{3} \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]The correct option is A
determine the orderd pair (8,-3)is a solytion to the linear pair
To answer this question, we need to evaluate if the ordered pair forms an identity with both equations. We need to substitute the values for x = 8, and y = -3 in both equations:
[tex]\frac{x}{2}+5y=-11\Rightarrow\frac{8}{2}+5(-3)=-11\Rightarrow4-15=-11\Rightarrow-11=-11[/tex]These values result in an equality in this equation. We need to evaluate the other equation:
[tex]6x-\frac{y}{6}=40\Rightarrow6\cdot(8)-(\frac{-3}{6})=40\Rightarrow48+\frac{1}{2}=\frac{97}{2}\ne-11[/tex]In this case, the values do not result in an equality in one of both equations.
Therefore, we have that the correct answer is the option B:
No, the proposed solution does not result in an equality in one of the two equations.
State the number of complex zeros and the possible number of real and imaginary zeros for each function. Then find all zeros. show all work
We have a cubic function
[tex]f(x)=x^3-3x^2-47x-87[/tex]One way to find all the zeros is by factoring, we can easily find the first zero using the divisors test if we have an independent term, at our case it's -87, one of the divisors may be a zero. The divisors of -87 is 1, 3, 29 and 87.
If we check for all of the divisors we will see that -3 is a zero. (Check with both signals).
If -3 is a zero, the D'Alembert theorem tells us that f(x) is divisible by (x+3), if we do that division we'll have a quadratic function where we can just apply the quadratic formula, then
There's a theorem that says that, if f(a) is a zero, i.e f(a) = 0, and f(x) is a polynomial, then f(x) is divisible by (x-a), in other words, we can divide f(x) by (x-a) and the rest of the division will be 0.
Therefore, let's divide our function by (x+3)
Then we can write our function as
[tex]f(x)=(x+3)(x^2-6x-29)[/tex]Look that now we have a quadratic function, and we can easily find its zeros, applying the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]We have a = 1, b = -6 and c = -29. Then
[tex]\begin{gathered} x=\frac{6\pm\sqrt[]{36+4\cdot29}}{2} \\ \\ x=\frac{6\pm\sqrt[]{156}}{2} \\ \\ x=\frac{6\pm2\sqrt[]{38}}{2} \\ \\ x=3\pm\sqrt[]{38} \end{gathered}[/tex]Now we have all the zeros of f(x), it's
[tex]\begin{gathered} x=-3 \\ \\ x=3+\sqrt[]{38} \\ \\ x=3-\sqrt[]{38} \end{gathered}[/tex]As we can see there's no complex zero, all the zeros are real numbers.
The max number of complex zeros is 2 because the complex zeros always come in pairs, so if we have 1 complex zero, automatically we have another, for a 3-degree equation, there's a maximum of 2 complex zeros and 1 real zero, or all the of them are real.
Then the correct answer is A)
what is the constant of proportionality in this proportional relationship? x 2 2-1/2 3 3-1/2 y 5/2 25/8 15/4 35/8. answer choices 4/5, 5/4, 4, 5
a proportional relationship has the following form:
yyy=
Sally Sue had spent all day preparing for the prom. All the glitz and the glamour of the evening fell apart as she stepped out of the limousine and her heel broke and she fell to the ground. Within minutes, news of her crashing fall had spread to the 550 people already at the prom. The function, p(t) = 550(1-e^-0.039t) where t represents the number of minutes after the fall, models the number of people who were already at the prom who heard the news.How many minutes does it take before all 550 people already at the prom hear the news ofthe great fall? Show your work.
We have the function
[tex]p(t)=550(1-e^{-0.039t})[/tex]Therefore we want to determine when we have
[tex]p(t_0)=550[/tex]It means that the term
[tex]e^{-0.039t}[/tex]Must go to zero, then let's forget the rest of the function for a sec and focus only on this term
[tex]e^{-0.039t}\rightarrow0[/tex]But for which value of t? When we have a decreasing exponential, it's interesting to input values that are multiples of the exponential coefficient, if we have 0.039 in the exponential, let's define that
[tex]\alpha=\frac{1}{0.039}[/tex]The inverse of the number, but why do that? look what happens when we do t = α
[tex]e^{-0.039t}\Rightarrow e^{-0.039\alpha}\Rightarrow e^{-1}=\frac{1}{e}[/tex]And when t = 2α
[tex]e^{-0.039t}\Rightarrow e^{-0.039\cdot2\alpha}\Rightarrow e^{-2}=\frac{1}{e^2}[/tex]We can write it in terms of e only.
And we can find for which value of α we have a small value that satisfies
[tex]e^{-0.039t}\approx0[/tex]Only using powers of e
Let's write some inverse powers of e:
[tex]\begin{gathered} \frac{1}{e}=0.368 \\ \\ \frac{1}{e^2}=0.135 \\ \\ \frac{1}{e^3}=0.05 \\ \\ \frac{1}{e^4}=0.02 \\ \\ \frac{1}{e^5}=0.006 \end{gathered}[/tex]See that at t = 5α we have a small value already, then if we input p(5α) we can get
[tex]\begin{gathered} p(5\alpha)=550(1-e^{-0.039\cdot5\alpha}) \\ \\ p(5\alpha)=550(1-0.006) \\ \\ p(5\alpha)=550(1-0.006) \\ \\ p(5\alpha)=550\cdot0.994 \\ \\ p(5\alpha)\approx547 \end{gathered}[/tex]That's already very close to 550, if we want a better approximation we can use t = 8α, which will result in 549.81, which is basically 550.
Therefore, we can use t = 5α and say that 3 people are not important for our case, and say that it's basically 550, or use t = 8α and get a very close value.
In both cases, the decimal answers would be
[tex]\begin{gathered} 5\alpha=\frac{5}{0.039}=128.2\text{ minutes (good approx)} \\ \\ 8\alpha=\frac{8}{0.039}=205.13\text{ minutes (even better approx)} \end{gathered}[/tex]Find the variance for the set of data: 22, 26, 17, 20, 20.The variance is
The variance of a given data set with size N is given by the formula:
[tex]\begin{gathered} \sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N(x_i-\mu)^2} \\ Var(X)=\sigma^2 \end{gathered}[/tex]Then, for the data set {22, 26, 17, 20, 20} and N = 5, we have:
[tex]\begin{gathered} \mu=\frac{22+26+17+20+20}{5}=21 \\ \sigma=\sqrt{\frac{1^2+5^2+(-4)^2+(-1)^2+(-1)^2}{5}}=\sqrt{\frac{44}{5}}=2\sqrt{\frac{11}{5}} \\ \therefore Var(X)=\frac{44}{5}=8.8 \end{gathered}[/tex]Classify the following conic section from its standard equation: 4y2 - 6x +16y - 21 = 0.My
it is a parabolla because only variable is quadratic and the other is linear.
Solve the system of two linear inequalities graphicallySysx-2y) -5x + 10Step 1 of 3: Graph the solution set of the first linear inequalityAnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (-)Enter two points on the boundary line:10-Select the region you wish to be shaded:Submit Answer
Given:
[tex]\begin{gathered} y\leq x-2 \\ \\ y>-5x+10 \end{gathered}[/tex]Find-: Solution set of the first linear inequality.
Sol:
Graph of first inequality is:
Graph of inequality of:
[tex]y>-5x+10[/tex]Graph of the given inequality is:
The solution of inequality is:
[tex]\begin{gathered} x=2 \\ y=0 \end{gathered}[/tex]The circle graph shows how the annual budget for a company is divided by department. If the amount budgeted for support, sales, and media combined is $25,000,000, what is the total annual budget?
Answer: $50,000,000
Explanation:
First, we add up the percentage of support, sales, and media covers. Given that:
Support = 23%
Sales = 22%
Media = 5%
The total percentage would be
[tex]23\%+22\%+5\%=50\%[/tex]This would mean that $25,000,000 covers half of the annual budget. The other half would be of the same amount, therefore, the total annual budget would be:
[tex]\begin{gathered} 50\%+50\%=100\% \\ \$25,000,000+\$25,000,000=\$50,000,000 \end{gathered}[/tex]The triangles are similar, solve for the question mark. A Z с ? 15 10 12 B X D E 8 8 18 12.5 0 24
Answer:
18
Explanation:
The triangles are similar if their sides are proportional. It meant that the ratio of AB to CD is equal to the ratio of AE to CE, so we can write the following equation:
[tex]\begin{gathered} \frac{AB}{CD}=\frac{AE}{CE} \\ \frac{15}{10}=\frac{AE}{12} \end{gathered}[/tex]So, we can solve for AE as:
[tex]\begin{gathered} \frac{15}{10}\cdot12=\frac{AE}{12}\cdot12 \\ 18=AE \end{gathered}[/tex]Therefore, the measure of AE is 18
the circle below is centered at the point (2,-1 ) and had a radius of length 3 what is its equation
The standard equation for a circle is
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where} \\ a=2 \\ b=-1 \\ r=\text{radius}=3 \\ (x-2)^2+(y-(-1))^2=3^2 \\ (x-2)^2+(y+1)^2=3^2 \\ \end{gathered}[/tex]